KILLED proof of input_P1f3xvBhv9.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) CpxTrsToCdtProof [UPPER BOUND(ID), 0 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), 10 ms] (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 1389 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 293 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 218 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 967 ms] (22) BEST (23) proven lower bound (24) LowerBoundPropagationProof [FINISHED, 0 ms] (25) BOUNDS(n^1, INF) (26) typed CpxTrs (27) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (28) CdtProblem (29) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CdtProblem (31) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (32) CpxRelTRS (33) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (34) CpxTRS (35) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (36) CpxWeightedTrs (37) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (38) CpxTypedWeightedTrs (39) CompletionProof [UPPER BOUND(ID), 0 ms] (40) CpxTypedWeightedCompleteTrs (41) NarrowingProof [BOTH BOUNDS(ID, ID), 281 ms] (42) CpxTypedWeightedCompleteTrs (43) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (44) CpxRNTS (45) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CpxRNTS (47) CompletionProof [UPPER BOUND(ID), 0 ms] (48) CpxTypedWeightedCompleteTrs (49) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (50) CpxRNTS (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CdtProblem (53) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CdtProblem (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CdtProblem (57) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 14 ms] (96) CdtProblem (97) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (106) CdtProblem (107) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9 ms] (110) CdtProblem (111) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtNarrowingProof [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) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (128) CdtProblem (129) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (132) CdtProblem (133) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (134) CdtProblem (135) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (138) CdtProblem (139) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (140) CdtProblem (141) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (144) CdtProblem (145) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (146) CdtProblem (147) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (148) CdtProblem (149) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (150) CdtProblem (151) CdtLeafRemovalProof [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), 4 ms] (160) CdtProblem (161) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 25 ms] (162) CdtProblem (163) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (164) CdtProblem (165) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (166) CdtProblem (167) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (168) CdtProblem (169) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (170) CdtProblem (171) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (172) CdtProblem (173) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (174) CdtProblem (175) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 3 ms] (176) CdtProblem (177) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (178) CdtProblem (179) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (180) CdtProblem (181) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (182) CdtProblem (183) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (184) CdtProblem (185) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 13 ms] (186) CdtProblem (187) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (188) CdtProblem (189) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (190) CdtProblem (191) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 21 ms] (192) CdtProblem (193) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (194) CdtProblem (195) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (196) CdtProblem (197) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (198) CdtProblem (199) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (200) CdtProblem (201) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (202) CdtProblem (203) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (204) CdtProblem (205) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 1 ms] (206) CdtProblem (207) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 7 ms] (208) CdtProblem (209) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (210) CdtProblem (211) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 3 ms] (212) CdtProblem (213) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (214) CdtProblem (215) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 12 ms] (216) CdtProblem (217) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (218) CdtProblem (219) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (220) CdtProblem (221) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 14 ms] (222) CdtProblem (223) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (224) CdtProblem (225) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 12 ms] (226) CdtProblem (227) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (228) CdtProblem (229) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 41 ms] (230) CdtProblem (231) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (232) CdtProblem (233) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (234) CdtProblem (235) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (236) CdtProblem (237) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 63 ms] (238) CdtProblem (239) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (240) CdtProblem (241) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 50 ms] (242) CdtProblem (243) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (244) CdtProblem (245) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 51 ms] (246) CdtProblem (247) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (248) CdtProblem (249) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 13 ms] (250) CdtProblem (251) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 12 ms] (252) CdtProblem (253) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 25 ms] (254) CdtProblem (255) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (256) CdtProblem (257) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (258) CpxWeightedTrs (259) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (260) CpxTypedWeightedTrs (261) CompletionProof [UPPER BOUND(ID), 0 ms] (262) CpxTypedWeightedCompleteTrs (263) NarrowingProof [BOTH BOUNDS(ID, ID), 14 ms] (264) CpxTypedWeightedCompleteTrs (265) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (266) CpxRNTS (267) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (268) CpxRNTS (269) CompletionProof [UPPER BOUND(ID), 0 ms] (270) CpxTypedWeightedCompleteTrs (271) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 5 ms] (272) CpxRNTS ---------------------------------------- (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, N) -> mark(N) a__U21(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__and(a__isNat(V1), isNat(V2)) a__isNat(s(V1)) -> a__isNat(V1) a__plus(N, 0) -> a__U11(a__isNat(N), N) a__plus(N, s(M)) -> a__U21(a__and(a__isNat(M), isNat(N)), M, N) mark(U11(X1, X2)) -> a__U11(mark(X1), X2) mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3) mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(isNat(X)) -> a__isNat(X) mark(tt) -> tt mark(s(X)) -> s(mark(X)) mark(0) -> 0 a__U11(X1, X2) -> U11(X1, X2) a__U21(X1, X2, X3) -> U21(X1, X2, X3) a__plus(X1, X2) -> plus(X1, X2) a__and(X1, X2) -> and(X1, X2) a__isNat(X) -> isNat(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, N) -> mark(N) a__U21(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__and(a__isNat(V1), isNat(V2)) a__isNat(s(V1)) -> a__isNat(V1) a__plus(N, 0') -> a__U11(a__isNat(N), N) a__plus(N, s(M)) -> a__U21(a__and(a__isNat(M), isNat(N)), M, N) mark(U11(X1, X2)) -> a__U11(mark(X1), X2) mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3) mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(isNat(X)) -> a__isNat(X) mark(tt) -> tt mark(s(X)) -> s(mark(X)) mark(0') -> 0' a__U11(X1, X2) -> U11(X1, X2) a__U21(X1, X2, X3) -> U21(X1, X2, X3) a__plus(X1, X2) -> plus(X1, X2) a__and(X1, X2) -> and(X1, X2) a__isNat(X) -> isNat(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, N) -> mark(N) a__U21(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__and(a__isNat(V1), isNat(V2)) a__isNat(s(V1)) -> a__isNat(V1) a__plus(N, 0) -> a__U11(a__isNat(N), N) a__plus(N, s(M)) -> a__U21(a__and(a__isNat(M), isNat(N)), M, N) mark(U11(X1, X2)) -> a__U11(mark(X1), X2) mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3) mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(isNat(X)) -> a__isNat(X) mark(tt) -> tt mark(s(X)) -> s(mark(X)) mark(0) -> 0 a__U11(X1, X2) -> U11(X1, X2) a__U21(X1, X2, X3) -> U21(X1, X2, X3) a__plus(X1, X2) -> plus(X1, X2) a__and(X1, X2) -> and(X1, X2) a__isNat(X) -> isNat(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) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__U11(z0, z1) -> c1 A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U21(z0, z1, z2) -> c4 A__AND(tt, z0) -> c5(MARK(z0)) A__AND(z0, z1) -> c6 A__ISNAT(0) -> c7 A__ISNAT(plus(z0, z1)) -> c8(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) A__ISNAT(z0) -> c10 A__PLUS(z0, 0) -> c11(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) A__PLUS(z0, z1) -> c13 MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(tt) -> c20 MARK(s(z0)) -> c21(MARK(z0)) MARK(0) -> c22 S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__U11(z0, z1) -> c1 A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U21(z0, z1, z2) -> c4 A__AND(tt, z0) -> c5(MARK(z0)) A__AND(z0, z1) -> c6 A__ISNAT(0) -> c7 A__ISNAT(plus(z0, z1)) -> c8(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) A__ISNAT(z0) -> c10 A__PLUS(z0, 0) -> c11(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) A__PLUS(z0, z1) -> c13 MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(tt) -> c20 MARK(s(z0)) -> c21(MARK(z0)) MARK(0) -> c22 K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_3, A__AND_2, A__ISNAT_1, A__PLUS_2, MARK_1 Compound Symbols: c_1, c1, c2_2, c3_2, c4, c5_1, c6, c7, c8_2, c9_1, c10, c11_2, c12_3, c13, c14_2, c15_2, c16_2, c17_2, c18_2, c19_1, c20, c21_1, c22 ---------------------------------------- (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) -> c(MARK(z0)) A__U11(z0, z1) -> c1 A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U21(z0, z1, z2) -> c4 A__AND(tt, z0) -> c5(MARK(z0)) A__AND(z0, z1) -> c6 A__ISNAT(0) -> c7 A__ISNAT(plus(z0, z1)) -> c8(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) A__ISNAT(z0) -> c10 A__PLUS(z0, 0) -> c11(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) A__PLUS(z0, z1) -> c13 MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(tt) -> c20 MARK(s(z0)) -> c21(MARK(z0)) MARK(0) -> c22 The (relative) TRS S consists of the following rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(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) -> c(MARK(z0)) A__U11(z0, z1) -> c1 A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U21(z0, z1, z2) -> c4 A__AND(tt, z0) -> c5(MARK(z0)) A__AND(z0, z1) -> c6 A__ISNAT(0') -> c7 A__ISNAT(plus(z0, z1)) -> c8(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) A__ISNAT(z0) -> c10 A__PLUS(z0, 0') -> c11(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) A__PLUS(z0, z1) -> c13 MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(tt) -> c20 MARK(s(z0)) -> c21(MARK(z0)) MARK(0') -> c22 The (relative) TRS S consists of the following rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0') -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(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) -> c(MARK(z0)) A__U11(z0, z1) -> c1 A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U21(z0, z1, z2) -> c4 A__AND(tt, z0) -> c5(MARK(z0)) A__AND(z0, z1) -> c6 A__ISNAT(0') -> c7 A__ISNAT(plus(z0, z1)) -> c8(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) A__ISNAT(z0) -> c10 A__PLUS(z0, 0') -> c11(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) A__PLUS(z0, z1) -> c13 MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(tt) -> c20 MARK(s(z0)) -> c21(MARK(z0)) MARK(0') -> c22 a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0') -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' Types: A__U11 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> c:c1 tt :: tt:0':plus:isNat:s:U11:U21:and c :: c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c:c1 MARK :: tt:0':plus:isNat:s:U11:U21:and -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c1 :: c:c1 A__U21 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> c2:c3:c4 c2 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c2:c3:c4 A__PLUS :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> c11:c12:c13 mark :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c3 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c2:c3:c4 c4 :: c2:c3:c4 A__AND :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> c5:c6 c5 :: c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c5:c6 c6 :: c5:c6 A__ISNAT :: tt:0':plus:isNat:s:U11:U21:and -> c7:c8:c9:c10 0' :: tt:0':plus:isNat:s:U11:U21:and c7 :: c7:c8:c9:c10 plus :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c8 :: c5:c6 -> c7:c8:c9:c10 -> c7:c8:c9:c10 a__isNat :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and isNat :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and s :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c9 :: c7:c8:c9:c10 -> c7:c8:c9:c10 c10 :: c7:c8:c9:c10 c11 :: c:c1 -> c7:c8:c9:c10 -> c11:c12:c13 c12 :: c2:c3:c4 -> c5:c6 -> c7:c8:c9:c10 -> c11:c12:c13 a__and :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c13 :: c11:c12:c13 U11 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c14 :: c:c1 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 U21 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c15 :: c2:c3:c4 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c16 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c17 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 and :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c18 :: c5:c6 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c19 :: c7:c8:c9:c10 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c20 :: c14:c15:c16:c17:c18:c19:c20:c21:c22 c21 :: c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c22 :: c14:c15:c16:c17:c18:c19:c20:c21:c22 a__U11 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and a__U21 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and a__plus :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and hole_c:c11_23 :: c:c1 hole_tt:0':plus:isNat:s:U11:U21:and2_23 :: tt:0':plus:isNat:s:U11:U21:and hole_c14:c15:c16:c17:c18:c19:c20:c21:c223_23 :: c14:c15:c16:c17:c18:c19:c20:c21:c22 hole_c2:c3:c44_23 :: c2:c3:c4 hole_c11:c12:c135_23 :: c11:c12:c13 hole_c5:c66_23 :: c5:c6 hole_c7:c8:c9:c107_23 :: c7:c8:c9:c10 gen_tt:0':plus:isNat:s:U11:U21:and8_23 :: Nat -> tt:0':plus:isNat:s:U11:U21:and gen_c14:c15:c16:c17:c18:c19:c20:c21:c229_23 :: Nat -> c14:c15:c16:c17:c18:c19:c20:c21:c22 gen_c7:c8:c9:c1010_23 :: Nat -> c7:c8:c9:c10 ---------------------------------------- (13) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: A__U11, MARK, A__U21, A__PLUS, mark, A__AND, A__ISNAT, a__isNat, a__and, a__U11, a__U21, a__plus They will be analysed ascendingly in the following order: A__U11 = MARK A__U11 = A__U21 A__U11 = A__PLUS A__U11 = A__AND A__U11 = A__ISNAT MARK = A__U21 MARK = A__PLUS mark < MARK MARK = A__AND MARK = A__ISNAT A__U21 = A__PLUS mark < A__U21 A__U21 = A__AND A__U21 = A__ISNAT A__PLUS = A__AND A__PLUS = A__ISNAT a__isNat < A__PLUS a__and < A__PLUS mark = a__isNat mark = a__and mark = a__U11 mark = a__U21 mark = a__plus A__AND = A__ISNAT a__isNat < A__ISNAT a__isNat = a__and a__isNat = a__U11 a__isNat = a__U21 a__isNat = a__plus a__and = a__U11 a__and = a__U21 a__and = a__plus a__U11 = a__U21 a__U11 = a__plus a__U21 = a__plus ---------------------------------------- (14) Obligation: Innermost TRS: Rules: A__U11(tt, z0) -> c(MARK(z0)) A__U11(z0, z1) -> c1 A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U21(z0, z1, z2) -> c4 A__AND(tt, z0) -> c5(MARK(z0)) A__AND(z0, z1) -> c6 A__ISNAT(0') -> c7 A__ISNAT(plus(z0, z1)) -> c8(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) A__ISNAT(z0) -> c10 A__PLUS(z0, 0') -> c11(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) A__PLUS(z0, z1) -> c13 MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(tt) -> c20 MARK(s(z0)) -> c21(MARK(z0)) MARK(0') -> c22 a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0') -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' Types: A__U11 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> c:c1 tt :: tt:0':plus:isNat:s:U11:U21:and c :: c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c:c1 MARK :: tt:0':plus:isNat:s:U11:U21:and -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c1 :: c:c1 A__U21 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> c2:c3:c4 c2 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c2:c3:c4 A__PLUS :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> c11:c12:c13 mark :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c3 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c2:c3:c4 c4 :: c2:c3:c4 A__AND :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> c5:c6 c5 :: c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c5:c6 c6 :: c5:c6 A__ISNAT :: tt:0':plus:isNat:s:U11:U21:and -> c7:c8:c9:c10 0' :: tt:0':plus:isNat:s:U11:U21:and c7 :: c7:c8:c9:c10 plus :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c8 :: c5:c6 -> c7:c8:c9:c10 -> c7:c8:c9:c10 a__isNat :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and isNat :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and s :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c9 :: c7:c8:c9:c10 -> c7:c8:c9:c10 c10 :: c7:c8:c9:c10 c11 :: c:c1 -> c7:c8:c9:c10 -> c11:c12:c13 c12 :: c2:c3:c4 -> c5:c6 -> c7:c8:c9:c10 -> c11:c12:c13 a__and :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c13 :: c11:c12:c13 U11 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c14 :: c:c1 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 U21 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c15 :: c2:c3:c4 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c16 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c17 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 and :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c18 :: c5:c6 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c19 :: c7:c8:c9:c10 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c20 :: c14:c15:c16:c17:c18:c19:c20:c21:c22 c21 :: c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c22 :: c14:c15:c16:c17:c18:c19:c20:c21:c22 a__U11 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and a__U21 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and a__plus :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and hole_c:c11_23 :: c:c1 hole_tt:0':plus:isNat:s:U11:U21:and2_23 :: tt:0':plus:isNat:s:U11:U21:and hole_c14:c15:c16:c17:c18:c19:c20:c21:c223_23 :: c14:c15:c16:c17:c18:c19:c20:c21:c22 hole_c2:c3:c44_23 :: c2:c3:c4 hole_c11:c12:c135_23 :: c11:c12:c13 hole_c5:c66_23 :: c5:c6 hole_c7:c8:c9:c107_23 :: c7:c8:c9:c10 gen_tt:0':plus:isNat:s:U11:U21:and8_23 :: Nat -> tt:0':plus:isNat:s:U11:U21:and gen_c14:c15:c16:c17:c18:c19:c20:c21:c229_23 :: Nat -> c14:c15:c16:c17:c18:c19:c20:c21:c22 gen_c7:c8:c9:c1010_23 :: Nat -> c7:c8:c9:c10 Generator Equations: gen_tt:0':plus:isNat:s:U11:U21:and8_23(0) <=> tt gen_tt:0':plus:isNat:s:U11:U21:and8_23(+(x, 1)) <=> plus(gen_tt:0':plus:isNat:s:U11:U21:and8_23(x), tt) gen_c14:c15:c16:c17:c18:c19:c20:c21:c229_23(0) <=> c19(c7) gen_c14:c15:c16:c17:c18:c19:c20:c21:c229_23(+(x, 1)) <=> c14(c(c19(c7)), gen_c14:c15:c16:c17:c18:c19:c20:c21:c229_23(x)) gen_c7:c8:c9:c1010_23(0) <=> c7 gen_c7:c8:c9:c1010_23(+(x, 1)) <=> c8(c5(c19(c7)), gen_c7:c8:c9:c1010_23(x)) The following defined symbols remain to be analysed: a__U11, A__U11, MARK, A__U21, A__PLUS, mark, A__AND, A__ISNAT, a__isNat, a__and, a__U21, a__plus They will be analysed ascendingly in the following order: A__U11 = MARK A__U11 = A__U21 A__U11 = A__PLUS A__U11 = A__AND A__U11 = A__ISNAT MARK = A__U21 MARK = A__PLUS mark < MARK MARK = A__AND MARK = A__ISNAT A__U21 = A__PLUS mark < A__U21 A__U21 = A__AND A__U21 = A__ISNAT A__PLUS = A__AND A__PLUS = A__ISNAT a__isNat < A__PLUS a__and < A__PLUS mark = a__isNat mark = a__and mark = a__U11 mark = a__U21 mark = a__plus A__AND = A__ISNAT a__isNat < A__ISNAT a__isNat = a__and a__isNat = a__U11 a__isNat = a__U21 a__isNat = a__plus a__and = a__U11 a__and = a__U21 a__and = a__plus a__U11 = a__U21 a__U11 = a__plus a__U21 = a__plus ---------------------------------------- (15) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: mark(gen_tt:0':plus:isNat:s:U11:U21:and8_23(n37924_23)) -> gen_tt:0':plus:isNat:s:U11:U21:and8_23(n37924_23), rt in Omega(0) Induction Base: mark(gen_tt:0':plus:isNat:s:U11:U21:and8_23(0)) ->_R^Omega(0) tt Induction Step: mark(gen_tt:0':plus:isNat:s:U11:U21:and8_23(+(n37924_23, 1))) ->_R^Omega(0) a__plus(mark(gen_tt:0':plus:isNat:s:U11:U21:and8_23(n37924_23)), mark(tt)) ->_IH a__plus(gen_tt:0':plus:isNat:s:U11:U21:and8_23(c37925_23), mark(tt)) ->_R^Omega(0) a__plus(gen_tt:0':plus:isNat:s:U11:U21:and8_23(n37924_23), tt) ->_R^Omega(0) plus(gen_tt:0':plus:isNat:s:U11:U21:and8_23(n37924_23), 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) -> c(MARK(z0)) A__U11(z0, z1) -> c1 A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U21(z0, z1, z2) -> c4 A__AND(tt, z0) -> c5(MARK(z0)) A__AND(z0, z1) -> c6 A__ISNAT(0') -> c7 A__ISNAT(plus(z0, z1)) -> c8(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) A__ISNAT(z0) -> c10 A__PLUS(z0, 0') -> c11(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) A__PLUS(z0, z1) -> c13 MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(tt) -> c20 MARK(s(z0)) -> c21(MARK(z0)) MARK(0') -> c22 a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0') -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' Types: A__U11 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> c:c1 tt :: tt:0':plus:isNat:s:U11:U21:and c :: c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c:c1 MARK :: tt:0':plus:isNat:s:U11:U21:and -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c1 :: c:c1 A__U21 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> c2:c3:c4 c2 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c2:c3:c4 A__PLUS :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> c11:c12:c13 mark :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c3 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c2:c3:c4 c4 :: c2:c3:c4 A__AND :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> c5:c6 c5 :: c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c5:c6 c6 :: c5:c6 A__ISNAT :: tt:0':plus:isNat:s:U11:U21:and -> c7:c8:c9:c10 0' :: tt:0':plus:isNat:s:U11:U21:and c7 :: c7:c8:c9:c10 plus :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c8 :: c5:c6 -> c7:c8:c9:c10 -> c7:c8:c9:c10 a__isNat :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and isNat :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and s :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c9 :: c7:c8:c9:c10 -> c7:c8:c9:c10 c10 :: c7:c8:c9:c10 c11 :: c:c1 -> c7:c8:c9:c10 -> c11:c12:c13 c12 :: c2:c3:c4 -> c5:c6 -> c7:c8:c9:c10 -> c11:c12:c13 a__and :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c13 :: c11:c12:c13 U11 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c14 :: c:c1 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 U21 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c15 :: c2:c3:c4 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c16 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c17 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 and :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c18 :: c5:c6 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c19 :: c7:c8:c9:c10 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c20 :: c14:c15:c16:c17:c18:c19:c20:c21:c22 c21 :: c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c22 :: c14:c15:c16:c17:c18:c19:c20:c21:c22 a__U11 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and a__U21 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and a__plus :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and hole_c:c11_23 :: c:c1 hole_tt:0':plus:isNat:s:U11:U21:and2_23 :: tt:0':plus:isNat:s:U11:U21:and hole_c14:c15:c16:c17:c18:c19:c20:c21:c223_23 :: c14:c15:c16:c17:c18:c19:c20:c21:c22 hole_c2:c3:c44_23 :: c2:c3:c4 hole_c11:c12:c135_23 :: c11:c12:c13 hole_c5:c66_23 :: c5:c6 hole_c7:c8:c9:c107_23 :: c7:c8:c9:c10 gen_tt:0':plus:isNat:s:U11:U21:and8_23 :: Nat -> tt:0':plus:isNat:s:U11:U21:and gen_c14:c15:c16:c17:c18:c19:c20:c21:c229_23 :: Nat -> c14:c15:c16:c17:c18:c19:c20:c21:c22 gen_c7:c8:c9:c1010_23 :: Nat -> c7:c8:c9:c10 Lemmas: mark(gen_tt:0':plus:isNat:s:U11:U21:and8_23(n37924_23)) -> gen_tt:0':plus:isNat:s:U11:U21:and8_23(n37924_23), rt in Omega(0) Generator Equations: gen_tt:0':plus:isNat:s:U11:U21:and8_23(0) <=> tt gen_tt:0':plus:isNat:s:U11:U21:and8_23(+(x, 1)) <=> plus(gen_tt:0':plus:isNat:s:U11:U21:and8_23(x), tt) gen_c14:c15:c16:c17:c18:c19:c20:c21:c229_23(0) <=> c19(c7) gen_c14:c15:c16:c17:c18:c19:c20:c21:c229_23(+(x, 1)) <=> c14(c(c19(c7)), gen_c14:c15:c16:c17:c18:c19:c20:c21:c229_23(x)) gen_c7:c8:c9:c1010_23(0) <=> c7 gen_c7:c8:c9:c1010_23(+(x, 1)) <=> c8(c5(c19(c7)), gen_c7:c8:c9:c1010_23(x)) The following defined symbols remain to be analysed: a__U21, A__U11, MARK, A__U21, A__PLUS, A__AND, A__ISNAT, a__isNat, a__and, a__U11, a__plus They will be analysed ascendingly in the following order: A__U11 = MARK A__U11 = A__U21 A__U11 = A__PLUS A__U11 = A__AND A__U11 = A__ISNAT MARK = A__U21 MARK = A__PLUS mark < MARK MARK = A__AND MARK = A__ISNAT A__U21 = A__PLUS mark < A__U21 A__U21 = A__AND A__U21 = A__ISNAT A__PLUS = A__AND A__PLUS = A__ISNAT a__isNat < A__PLUS a__and < A__PLUS mark = a__isNat mark = a__and mark = a__U11 mark = a__U21 mark = a__plus A__AND = A__ISNAT a__isNat < A__ISNAT a__isNat = a__and a__isNat = a__U11 a__isNat = a__U21 a__isNat = a__plus a__and = a__U11 a__and = a__U21 a__and = a__plus a__U11 = a__U21 a__U11 = a__plus a__U21 = a__plus ---------------------------------------- (17) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: a__isNat(gen_tt:0':plus:isNat:s:U11:U21:and8_23(+(1, n50979_23))) -> *11_23, rt in Omega(0) Induction Base: a__isNat(gen_tt:0':plus:isNat:s:U11:U21:and8_23(+(1, 0))) Induction Step: a__isNat(gen_tt:0':plus:isNat:s:U11:U21:and8_23(+(1, +(n50979_23, 1)))) ->_R^Omega(0) a__and(a__isNat(gen_tt:0':plus:isNat:s:U11:U21:and8_23(+(1, n50979_23))), isNat(tt)) ->_IH a__and(*11_23, isNat(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) -> c(MARK(z0)) A__U11(z0, z1) -> c1 A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U21(z0, z1, z2) -> c4 A__AND(tt, z0) -> c5(MARK(z0)) A__AND(z0, z1) -> c6 A__ISNAT(0') -> c7 A__ISNAT(plus(z0, z1)) -> c8(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) A__ISNAT(z0) -> c10 A__PLUS(z0, 0') -> c11(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) A__PLUS(z0, z1) -> c13 MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(tt) -> c20 MARK(s(z0)) -> c21(MARK(z0)) MARK(0') -> c22 a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0') -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' Types: A__U11 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> c:c1 tt :: tt:0':plus:isNat:s:U11:U21:and c :: c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c:c1 MARK :: tt:0':plus:isNat:s:U11:U21:and -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c1 :: c:c1 A__U21 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> c2:c3:c4 c2 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c2:c3:c4 A__PLUS :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> c11:c12:c13 mark :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c3 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c2:c3:c4 c4 :: c2:c3:c4 A__AND :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> c5:c6 c5 :: c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c5:c6 c6 :: c5:c6 A__ISNAT :: tt:0':plus:isNat:s:U11:U21:and -> c7:c8:c9:c10 0' :: tt:0':plus:isNat:s:U11:U21:and c7 :: c7:c8:c9:c10 plus :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c8 :: c5:c6 -> c7:c8:c9:c10 -> c7:c8:c9:c10 a__isNat :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and isNat :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and s :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c9 :: c7:c8:c9:c10 -> c7:c8:c9:c10 c10 :: c7:c8:c9:c10 c11 :: c:c1 -> c7:c8:c9:c10 -> c11:c12:c13 c12 :: c2:c3:c4 -> c5:c6 -> c7:c8:c9:c10 -> c11:c12:c13 a__and :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c13 :: c11:c12:c13 U11 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c14 :: c:c1 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 U21 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c15 :: c2:c3:c4 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c16 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c17 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 and :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c18 :: c5:c6 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c19 :: c7:c8:c9:c10 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c20 :: c14:c15:c16:c17:c18:c19:c20:c21:c22 c21 :: c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c22 :: c14:c15:c16:c17:c18:c19:c20:c21:c22 a__U11 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and a__U21 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and a__plus :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and hole_c:c11_23 :: c:c1 hole_tt:0':plus:isNat:s:U11:U21:and2_23 :: tt:0':plus:isNat:s:U11:U21:and hole_c14:c15:c16:c17:c18:c19:c20:c21:c223_23 :: c14:c15:c16:c17:c18:c19:c20:c21:c22 hole_c2:c3:c44_23 :: c2:c3:c4 hole_c11:c12:c135_23 :: c11:c12:c13 hole_c5:c66_23 :: c5:c6 hole_c7:c8:c9:c107_23 :: c7:c8:c9:c10 gen_tt:0':plus:isNat:s:U11:U21:and8_23 :: Nat -> tt:0':plus:isNat:s:U11:U21:and gen_c14:c15:c16:c17:c18:c19:c20:c21:c229_23 :: Nat -> c14:c15:c16:c17:c18:c19:c20:c21:c22 gen_c7:c8:c9:c1010_23 :: Nat -> c7:c8:c9:c10 Lemmas: mark(gen_tt:0':plus:isNat:s:U11:U21:and8_23(n37924_23)) -> gen_tt:0':plus:isNat:s:U11:U21:and8_23(n37924_23), rt in Omega(0) a__isNat(gen_tt:0':plus:isNat:s:U11:U21:and8_23(+(1, n50979_23))) -> *11_23, rt in Omega(0) Generator Equations: gen_tt:0':plus:isNat:s:U11:U21:and8_23(0) <=> tt gen_tt:0':plus:isNat:s:U11:U21:and8_23(+(x, 1)) <=> plus(gen_tt:0':plus:isNat:s:U11:U21:and8_23(x), tt) gen_c14:c15:c16:c17:c18:c19:c20:c21:c229_23(0) <=> c19(c7) gen_c14:c15:c16:c17:c18:c19:c20:c21:c229_23(+(x, 1)) <=> c14(c(c19(c7)), gen_c14:c15:c16:c17:c18:c19:c20:c21:c229_23(x)) gen_c7:c8:c9:c1010_23(0) <=> c7 gen_c7:c8:c9:c1010_23(+(x, 1)) <=> c8(c5(c19(c7)), gen_c7:c8:c9:c1010_23(x)) The following defined symbols remain to be analysed: a__and, A__U11, MARK, A__U21, A__PLUS, mark, A__AND, A__ISNAT, a__U11, a__U21, a__plus They will be analysed ascendingly in the following order: A__U11 = MARK A__U11 = A__U21 A__U11 = A__PLUS A__U11 = A__AND A__U11 = A__ISNAT MARK = A__U21 MARK = A__PLUS mark < MARK MARK = A__AND MARK = A__ISNAT A__U21 = A__PLUS mark < A__U21 A__U21 = A__AND A__U21 = A__ISNAT A__PLUS = A__AND A__PLUS = A__ISNAT a__isNat < A__PLUS a__and < A__PLUS mark = a__isNat mark = a__and mark = a__U11 mark = a__U21 mark = a__plus A__AND = A__ISNAT a__isNat < A__ISNAT a__isNat = a__and a__isNat = a__U11 a__isNat = a__U21 a__isNat = a__plus a__and = a__U11 a__and = a__U21 a__and = a__plus a__U11 = a__U21 a__U11 = a__plus a__U21 = a__plus ---------------------------------------- (19) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: mark(gen_tt:0':plus:isNat:s:U11:U21:and8_23(n52716_23)) -> gen_tt:0':plus:isNat:s:U11:U21:and8_23(n52716_23), rt in Omega(0) Induction Base: mark(gen_tt:0':plus:isNat:s:U11:U21:and8_23(0)) ->_R^Omega(0) tt Induction Step: mark(gen_tt:0':plus:isNat:s:U11:U21:and8_23(+(n52716_23, 1))) ->_R^Omega(0) a__plus(mark(gen_tt:0':plus:isNat:s:U11:U21:and8_23(n52716_23)), mark(tt)) ->_IH a__plus(gen_tt:0':plus:isNat:s:U11:U21:and8_23(c52717_23), mark(tt)) ->_R^Omega(0) a__plus(gen_tt:0':plus:isNat:s:U11:U21:and8_23(n52716_23), tt) ->_R^Omega(0) plus(gen_tt:0':plus:isNat:s:U11:U21:and8_23(n52716_23), 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) -> c(MARK(z0)) A__U11(z0, z1) -> c1 A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U21(z0, z1, z2) -> c4 A__AND(tt, z0) -> c5(MARK(z0)) A__AND(z0, z1) -> c6 A__ISNAT(0') -> c7 A__ISNAT(plus(z0, z1)) -> c8(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) A__ISNAT(z0) -> c10 A__PLUS(z0, 0') -> c11(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) A__PLUS(z0, z1) -> c13 MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(tt) -> c20 MARK(s(z0)) -> c21(MARK(z0)) MARK(0') -> c22 a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0') -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' Types: A__U11 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> c:c1 tt :: tt:0':plus:isNat:s:U11:U21:and c :: c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c:c1 MARK :: tt:0':plus:isNat:s:U11:U21:and -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c1 :: c:c1 A__U21 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> c2:c3:c4 c2 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c2:c3:c4 A__PLUS :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> c11:c12:c13 mark :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c3 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c2:c3:c4 c4 :: c2:c3:c4 A__AND :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> c5:c6 c5 :: c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c5:c6 c6 :: c5:c6 A__ISNAT :: tt:0':plus:isNat:s:U11:U21:and -> c7:c8:c9:c10 0' :: tt:0':plus:isNat:s:U11:U21:and c7 :: c7:c8:c9:c10 plus :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c8 :: c5:c6 -> c7:c8:c9:c10 -> c7:c8:c9:c10 a__isNat :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and isNat :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and s :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c9 :: c7:c8:c9:c10 -> c7:c8:c9:c10 c10 :: c7:c8:c9:c10 c11 :: c:c1 -> c7:c8:c9:c10 -> c11:c12:c13 c12 :: c2:c3:c4 -> c5:c6 -> c7:c8:c9:c10 -> c11:c12:c13 a__and :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c13 :: c11:c12:c13 U11 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c14 :: c:c1 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 U21 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c15 :: c2:c3:c4 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c16 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c17 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 and :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c18 :: c5:c6 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c19 :: c7:c8:c9:c10 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c20 :: c14:c15:c16:c17:c18:c19:c20:c21:c22 c21 :: c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c22 :: c14:c15:c16:c17:c18:c19:c20:c21:c22 a__U11 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and a__U21 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and a__plus :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and hole_c:c11_23 :: c:c1 hole_tt:0':plus:isNat:s:U11:U21:and2_23 :: tt:0':plus:isNat:s:U11:U21:and hole_c14:c15:c16:c17:c18:c19:c20:c21:c223_23 :: c14:c15:c16:c17:c18:c19:c20:c21:c22 hole_c2:c3:c44_23 :: c2:c3:c4 hole_c11:c12:c135_23 :: c11:c12:c13 hole_c5:c66_23 :: c5:c6 hole_c7:c8:c9:c107_23 :: c7:c8:c9:c10 gen_tt:0':plus:isNat:s:U11:U21:and8_23 :: Nat -> tt:0':plus:isNat:s:U11:U21:and gen_c14:c15:c16:c17:c18:c19:c20:c21:c229_23 :: Nat -> c14:c15:c16:c17:c18:c19:c20:c21:c22 gen_c7:c8:c9:c1010_23 :: Nat -> c7:c8:c9:c10 Lemmas: mark(gen_tt:0':plus:isNat:s:U11:U21:and8_23(n52716_23)) -> gen_tt:0':plus:isNat:s:U11:U21:and8_23(n52716_23), rt in Omega(0) a__isNat(gen_tt:0':plus:isNat:s:U11:U21:and8_23(+(1, n50979_23))) -> *11_23, rt in Omega(0) Generator Equations: gen_tt:0':plus:isNat:s:U11:U21:and8_23(0) <=> tt gen_tt:0':plus:isNat:s:U11:U21:and8_23(+(x, 1)) <=> plus(gen_tt:0':plus:isNat:s:U11:U21:and8_23(x), tt) gen_c14:c15:c16:c17:c18:c19:c20:c21:c229_23(0) <=> c19(c7) gen_c14:c15:c16:c17:c18:c19:c20:c21:c229_23(+(x, 1)) <=> c14(c(c19(c7)), gen_c14:c15:c16:c17:c18:c19:c20:c21:c229_23(x)) gen_c7:c8:c9:c1010_23(0) <=> c7 gen_c7:c8:c9:c1010_23(+(x, 1)) <=> c8(c5(c19(c7)), gen_c7:c8:c9:c1010_23(x)) The following defined symbols remain to be analysed: a__U21, A__U11, MARK, A__U21, A__PLUS, A__AND, A__ISNAT, a__plus They will be analysed ascendingly in the following order: A__U11 = MARK A__U11 = A__U21 A__U11 = A__PLUS A__U11 = A__AND A__U11 = A__ISNAT MARK = A__U21 MARK = A__PLUS mark < MARK MARK = A__AND MARK = A__ISNAT A__U21 = A__PLUS mark < A__U21 A__U21 = A__AND A__U21 = A__ISNAT A__PLUS = A__AND A__PLUS = A__ISNAT a__isNat < A__PLUS a__and < A__PLUS mark = a__isNat mark = a__and mark = a__U11 mark = a__U21 mark = a__plus A__AND = A__ISNAT a__isNat < A__ISNAT a__isNat = a__and a__isNat = a__U11 a__isNat = a__U21 a__isNat = a__plus a__and = a__U11 a__and = a__U21 a__and = a__plus a__U11 = a__U21 a__U11 = a__plus a__U21 = a__plus ---------------------------------------- (21) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: MARK(gen_tt:0':plus:isNat:s:U11:U21:and8_23(+(1, n66081_23))) -> *11_23, rt in Omega(n66081_23) Induction Base: MARK(gen_tt:0':plus:isNat:s:U11:U21:and8_23(+(1, 0))) Induction Step: MARK(gen_tt:0':plus:isNat:s:U11:U21:and8_23(+(1, +(n66081_23, 1)))) ->_R^Omega(1) c16(A__PLUS(mark(gen_tt:0':plus:isNat:s:U11:U21:and8_23(+(1, n66081_23))), mark(tt)), MARK(gen_tt:0':plus:isNat:s:U11:U21:and8_23(+(1, n66081_23)))) ->_L^Omega(0) c16(A__PLUS(gen_tt:0':plus:isNat:s:U11:U21:and8_23(+(1, n66081_23)), mark(tt)), MARK(gen_tt:0':plus:isNat:s:U11:U21:and8_23(+(1, n66081_23)))) ->_L^Omega(0) c16(A__PLUS(gen_tt:0':plus:isNat:s:U11:U21:and8_23(+(1, n66081_23)), gen_tt:0':plus:isNat:s:U11:U21:and8_23(0)), MARK(gen_tt:0':plus:isNat:s:U11:U21:and8_23(+(1, n66081_23)))) ->_R^Omega(1) c16(c13, MARK(gen_tt:0':plus:isNat:s:U11:U21:and8_23(+(1, n66081_23)))) ->_IH c16(c13, *11_23) 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) -> c(MARK(z0)) A__U11(z0, z1) -> c1 A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U21(z0, z1, z2) -> c4 A__AND(tt, z0) -> c5(MARK(z0)) A__AND(z0, z1) -> c6 A__ISNAT(0') -> c7 A__ISNAT(plus(z0, z1)) -> c8(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) A__ISNAT(z0) -> c10 A__PLUS(z0, 0') -> c11(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) A__PLUS(z0, z1) -> c13 MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(tt) -> c20 MARK(s(z0)) -> c21(MARK(z0)) MARK(0') -> c22 a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0') -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' Types: A__U11 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> c:c1 tt :: tt:0':plus:isNat:s:U11:U21:and c :: c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c:c1 MARK :: tt:0':plus:isNat:s:U11:U21:and -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c1 :: c:c1 A__U21 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> c2:c3:c4 c2 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c2:c3:c4 A__PLUS :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> c11:c12:c13 mark :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c3 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c2:c3:c4 c4 :: c2:c3:c4 A__AND :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> c5:c6 c5 :: c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c5:c6 c6 :: c5:c6 A__ISNAT :: tt:0':plus:isNat:s:U11:U21:and -> c7:c8:c9:c10 0' :: tt:0':plus:isNat:s:U11:U21:and c7 :: c7:c8:c9:c10 plus :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c8 :: c5:c6 -> c7:c8:c9:c10 -> c7:c8:c9:c10 a__isNat :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and isNat :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and s :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c9 :: c7:c8:c9:c10 -> c7:c8:c9:c10 c10 :: c7:c8:c9:c10 c11 :: c:c1 -> c7:c8:c9:c10 -> c11:c12:c13 c12 :: c2:c3:c4 -> c5:c6 -> c7:c8:c9:c10 -> c11:c12:c13 a__and :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c13 :: c11:c12:c13 U11 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c14 :: c:c1 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 U21 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c15 :: c2:c3:c4 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c16 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c17 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 and :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c18 :: c5:c6 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c19 :: c7:c8:c9:c10 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c20 :: c14:c15:c16:c17:c18:c19:c20:c21:c22 c21 :: c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c22 :: c14:c15:c16:c17:c18:c19:c20:c21:c22 a__U11 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and a__U21 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and a__plus :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and hole_c:c11_23 :: c:c1 hole_tt:0':plus:isNat:s:U11:U21:and2_23 :: tt:0':plus:isNat:s:U11:U21:and hole_c14:c15:c16:c17:c18:c19:c20:c21:c223_23 :: c14:c15:c16:c17:c18:c19:c20:c21:c22 hole_c2:c3:c44_23 :: c2:c3:c4 hole_c11:c12:c135_23 :: c11:c12:c13 hole_c5:c66_23 :: c5:c6 hole_c7:c8:c9:c107_23 :: c7:c8:c9:c10 gen_tt:0':plus:isNat:s:U11:U21:and8_23 :: Nat -> tt:0':plus:isNat:s:U11:U21:and gen_c14:c15:c16:c17:c18:c19:c20:c21:c229_23 :: Nat -> c14:c15:c16:c17:c18:c19:c20:c21:c22 gen_c7:c8:c9:c1010_23 :: Nat -> c7:c8:c9:c10 Lemmas: mark(gen_tt:0':plus:isNat:s:U11:U21:and8_23(n52716_23)) -> gen_tt:0':plus:isNat:s:U11:U21:and8_23(n52716_23), rt in Omega(0) a__isNat(gen_tt:0':plus:isNat:s:U11:U21:and8_23(+(1, n50979_23))) -> *11_23, rt in Omega(0) Generator Equations: gen_tt:0':plus:isNat:s:U11:U21:and8_23(0) <=> tt gen_tt:0':plus:isNat:s:U11:U21:and8_23(+(x, 1)) <=> plus(gen_tt:0':plus:isNat:s:U11:U21:and8_23(x), tt) gen_c14:c15:c16:c17:c18:c19:c20:c21:c229_23(0) <=> c19(c7) gen_c14:c15:c16:c17:c18:c19:c20:c21:c229_23(+(x, 1)) <=> c14(c(c19(c7)), gen_c14:c15:c16:c17:c18:c19:c20:c21:c229_23(x)) gen_c7:c8:c9:c1010_23(0) <=> c7 gen_c7:c8:c9:c1010_23(+(x, 1)) <=> c8(c5(c19(c7)), gen_c7:c8:c9:c1010_23(x)) The following defined symbols remain to be analysed: MARK, A__U11, A__U21, A__PLUS, A__AND, A__ISNAT They will be analysed ascendingly in the following order: A__U11 = MARK A__U11 = A__U21 A__U11 = A__PLUS A__U11 = A__AND A__U11 = A__ISNAT MARK = A__U21 MARK = A__PLUS MARK = A__AND MARK = A__ISNAT A__U21 = A__PLUS A__U21 = A__AND A__U21 = A__ISNAT A__PLUS = A__AND A__PLUS = A__ISNAT A__AND = A__ISNAT ---------------------------------------- (24) LowerBoundPropagationProof (FINISHED) Propagated lower bound. ---------------------------------------- (25) BOUNDS(n^1, INF) ---------------------------------------- (26) Obligation: Innermost TRS: Rules: A__U11(tt, z0) -> c(MARK(z0)) A__U11(z0, z1) -> c1 A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U21(z0, z1, z2) -> c4 A__AND(tt, z0) -> c5(MARK(z0)) A__AND(z0, z1) -> c6 A__ISNAT(0') -> c7 A__ISNAT(plus(z0, z1)) -> c8(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) A__ISNAT(z0) -> c10 A__PLUS(z0, 0') -> c11(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) A__PLUS(z0, z1) -> c13 MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(tt) -> c20 MARK(s(z0)) -> c21(MARK(z0)) MARK(0') -> c22 a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0') -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' Types: A__U11 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> c:c1 tt :: tt:0':plus:isNat:s:U11:U21:and c :: c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c:c1 MARK :: tt:0':plus:isNat:s:U11:U21:and -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c1 :: c:c1 A__U21 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> c2:c3:c4 c2 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c2:c3:c4 A__PLUS :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> c11:c12:c13 mark :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c3 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c2:c3:c4 c4 :: c2:c3:c4 A__AND :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> c5:c6 c5 :: c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c5:c6 c6 :: c5:c6 A__ISNAT :: tt:0':plus:isNat:s:U11:U21:and -> c7:c8:c9:c10 0' :: tt:0':plus:isNat:s:U11:U21:and c7 :: c7:c8:c9:c10 plus :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c8 :: c5:c6 -> c7:c8:c9:c10 -> c7:c8:c9:c10 a__isNat :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and isNat :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and s :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c9 :: c7:c8:c9:c10 -> c7:c8:c9:c10 c10 :: c7:c8:c9:c10 c11 :: c:c1 -> c7:c8:c9:c10 -> c11:c12:c13 c12 :: c2:c3:c4 -> c5:c6 -> c7:c8:c9:c10 -> c11:c12:c13 a__and :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c13 :: c11:c12:c13 U11 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c14 :: c:c1 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 U21 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c15 :: c2:c3:c4 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c16 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c17 :: c11:c12:c13 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 and :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and c18 :: c5:c6 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c19 :: c7:c8:c9:c10 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c20 :: c14:c15:c16:c17:c18:c19:c20:c21:c22 c21 :: c14:c15:c16:c17:c18:c19:c20:c21:c22 -> c14:c15:c16:c17:c18:c19:c20:c21:c22 c22 :: c14:c15:c16:c17:c18:c19:c20:c21:c22 a__U11 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and a__U21 :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and a__plus :: tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and -> tt:0':plus:isNat:s:U11:U21:and hole_c:c11_23 :: c:c1 hole_tt:0':plus:isNat:s:U11:U21:and2_23 :: tt:0':plus:isNat:s:U11:U21:and hole_c14:c15:c16:c17:c18:c19:c20:c21:c223_23 :: c14:c15:c16:c17:c18:c19:c20:c21:c22 hole_c2:c3:c44_23 :: c2:c3:c4 hole_c11:c12:c135_23 :: c11:c12:c13 hole_c5:c66_23 :: c5:c6 hole_c7:c8:c9:c107_23 :: c7:c8:c9:c10 gen_tt:0':plus:isNat:s:U11:U21:and8_23 :: Nat -> tt:0':plus:isNat:s:U11:U21:and gen_c14:c15:c16:c17:c18:c19:c20:c21:c229_23 :: Nat -> c14:c15:c16:c17:c18:c19:c20:c21:c22 gen_c7:c8:c9:c1010_23 :: Nat -> c7:c8:c9:c10 Lemmas: mark(gen_tt:0':plus:isNat:s:U11:U21:and8_23(n52716_23)) -> gen_tt:0':plus:isNat:s:U11:U21:and8_23(n52716_23), rt in Omega(0) a__isNat(gen_tt:0':plus:isNat:s:U11:U21:and8_23(+(1, n50979_23))) -> *11_23, rt in Omega(0) MARK(gen_tt:0':plus:isNat:s:U11:U21:and8_23(+(1, n66081_23))) -> *11_23, rt in Omega(n66081_23) Generator Equations: gen_tt:0':plus:isNat:s:U11:U21:and8_23(0) <=> tt gen_tt:0':plus:isNat:s:U11:U21:and8_23(+(x, 1)) <=> plus(gen_tt:0':plus:isNat:s:U11:U21:and8_23(x), tt) gen_c14:c15:c16:c17:c18:c19:c20:c21:c229_23(0) <=> c19(c7) gen_c14:c15:c16:c17:c18:c19:c20:c21:c229_23(+(x, 1)) <=> c14(c(c19(c7)), gen_c14:c15:c16:c17:c18:c19:c20:c21:c229_23(x)) gen_c7:c8:c9:c1010_23(0) <=> c7 gen_c7:c8:c9:c1010_23(+(x, 1)) <=> c8(c5(c19(c7)), gen_c7:c8:c9:c1010_23(x)) The following defined symbols remain to be analysed: A__U11, A__U21, A__PLUS, A__AND, A__ISNAT They will be analysed ascendingly in the following order: A__U11 = MARK A__U11 = A__U21 A__U11 = A__PLUS A__U11 = A__AND A__U11 = A__ISNAT MARK = A__U21 MARK = A__PLUS MARK = A__AND MARK = A__ISNAT A__U21 = A__PLUS A__U21 = A__AND A__U21 = A__ISNAT A__PLUS = A__AND A__PLUS = A__ISNAT A__AND = A__ISNAT ---------------------------------------- (27) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (28) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__U11(z0, z1) -> c1 A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U21(z0, z1, z2) -> c4 A__AND(tt, z0) -> c5(MARK(z0)) A__AND(z0, z1) -> c6 A__ISNAT(0) -> c7 A__ISNAT(plus(z0, z1)) -> c8(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) A__ISNAT(z0) -> c10 A__PLUS(z0, 0) -> c11(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) A__PLUS(z0, z1) -> c13 MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(tt) -> c20 MARK(s(z0)) -> c21(MARK(z0)) MARK(0) -> c22 S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__U11(z0, z1) -> c1 A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U21(z0, z1, z2) -> c4 A__AND(tt, z0) -> c5(MARK(z0)) A__AND(z0, z1) -> c6 A__ISNAT(0) -> c7 A__ISNAT(plus(z0, z1)) -> c8(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) A__ISNAT(z0) -> c10 A__PLUS(z0, 0) -> c11(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) A__PLUS(z0, z1) -> c13 MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(tt) -> c20 MARK(s(z0)) -> c21(MARK(z0)) MARK(0) -> c22 K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_3, A__AND_2, A__ISNAT_1, A__PLUS_2, MARK_1 Compound Symbols: c_1, c1, c2_2, c3_2, c4, c5_1, c6, c7, c8_2, c9_1, c10, c11_2, c12_3, c13, c14_2, c15_2, c16_2, c17_2, c18_2, c19_1, c20, c21_1, c22 ---------------------------------------- (29) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 8 trailing nodes: A__PLUS(z0, z1) -> c13 MARK(0) -> c22 A__U11(z0, z1) -> c1 A__U21(z0, z1, z2) -> c4 MARK(tt) -> c20 A__ISNAT(0) -> c7 A__AND(z0, z1) -> c6 A__ISNAT(z0) -> c10 ---------------------------------------- (30) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c8(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) A__PLUS(z0, 0) -> c11(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c8(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) A__PLUS(z0, 0) -> c11(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_3, A__AND_2, A__ISNAT_1, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_2, c3_2, c5_1, c8_2, c9_1, c11_2, c12_3, c14_2, c15_2, c16_2, c17_2, c18_2, c19_1, c21_1 ---------------------------------------- (31) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (32) 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) -> c(MARK(z0)) A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c8(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) A__PLUS(z0, 0) -> c11(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) The (relative) TRS S consists of the following rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Rewrite Strategy: INNERMOST ---------------------------------------- (33) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (34) 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) -> c(MARK(z0)) A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c8(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) A__PLUS(z0, 0) -> c11(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (35) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (36) 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) -> c(MARK(z0)) [1] A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1] A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1] A__AND(tt, z0) -> c5(MARK(z0)) [1] A__ISNAT(plus(z0, z1)) -> c8(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) [1] A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) [1] A__PLUS(z0, 0) -> c11(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) [1] A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) [1] MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) [1] MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) [1] MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) [1] MARK(isNat(z0)) -> c19(A__ISNAT(z0)) [1] MARK(s(z0)) -> c21(MARK(z0)) [1] a__U11(tt, z0) -> mark(z0) [0] a__U11(z0, z1) -> U11(z0, z1) [0] a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0] a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) [0] a__isNat(s(z0)) -> a__isNat(z0) [0] a__isNat(z0) -> isNat(z0) [0] a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) [0] a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) [0] a__plus(z0, z1) -> plus(z0, z1) [0] mark(U11(z0, z1)) -> a__U11(mark(z0), z1) [0] mark(U21(z0, z1, z2)) -> a__U21(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(isNat(z0)) -> a__isNat(z0) [0] mark(tt) -> tt [0] mark(s(z0)) -> s(mark(z0)) [0] mark(0) -> 0 [0] Rewrite Strategy: INNERMOST ---------------------------------------- (37) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (38) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__U11(tt, z0) -> c(MARK(z0)) [1] A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1] A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1] A__AND(tt, z0) -> c5(MARK(z0)) [1] A__ISNAT(plus(z0, z1)) -> c8(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) [1] A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) [1] A__PLUS(z0, 0) -> c11(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) [1] A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) [1] MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) [1] MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) [1] MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) [1] MARK(isNat(z0)) -> c19(A__ISNAT(z0)) [1] MARK(s(z0)) -> c21(MARK(z0)) [1] a__U11(tt, z0) -> mark(z0) [0] a__U11(z0, z1) -> U11(z0, z1) [0] a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0] a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) [0] a__isNat(s(z0)) -> a__isNat(z0) [0] a__isNat(z0) -> isNat(z0) [0] a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) [0] a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) [0] a__plus(z0, z1) -> plus(z0, z1) [0] mark(U11(z0, z1)) -> a__U11(mark(z0), z1) [0] mark(U21(z0, z1, z2)) -> a__U21(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(isNat(z0)) -> a__isNat(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:isNat:s:0:U11:U21:and -> tt:plus:isNat:s:0:U11:U21:and -> c tt :: tt:plus:isNat:s:0:U11:U21:and c :: c14:c15:c16:c17:c18:c19:c21 -> c MARK :: tt:plus:isNat:s:0:U11:U21:and -> c14:c15:c16:c17:c18:c19:c21 A__U21 :: tt:plus:isNat:s:0:U11:U21:and -> tt:plus:isNat:s:0:U11:U21:and -> tt:plus:isNat:s:0:U11:U21:and -> c2:c3 c2 :: c11:c12 -> c14:c15:c16:c17:c18:c19:c21 -> c2:c3 A__PLUS :: tt:plus:isNat:s:0:U11:U21:and -> tt:plus:isNat:s:0:U11:U21:and -> c11:c12 mark :: tt:plus:isNat:s:0:U11:U21:and -> tt:plus:isNat:s:0:U11:U21:and c3 :: c11:c12 -> c14:c15:c16:c17:c18:c19:c21 -> c2:c3 A__AND :: tt:plus:isNat:s:0:U11:U21:and -> tt:plus:isNat:s:0:U11:U21:and -> c5 c5 :: c14:c15:c16:c17:c18:c19:c21 -> c5 A__ISNAT :: tt:plus:isNat:s:0:U11:U21:and -> c8:c9 plus :: tt:plus:isNat:s:0:U11:U21:and -> tt:plus:isNat:s:0:U11:U21:and -> tt:plus:isNat:s:0:U11:U21:and c8 :: c5 -> c8:c9 -> c8:c9 a__isNat :: tt:plus:isNat:s:0:U11:U21:and -> tt:plus:isNat:s:0:U11:U21:and isNat :: tt:plus:isNat:s:0:U11:U21:and -> tt:plus:isNat:s:0:U11:U21:and s :: tt:plus:isNat:s:0:U11:U21:and -> tt:plus:isNat:s:0:U11:U21:and c9 :: c8:c9 -> c8:c9 0 :: tt:plus:isNat:s:0:U11:U21:and c11 :: c -> c8:c9 -> c11:c12 c12 :: c2:c3 -> c5 -> c8:c9 -> c11:c12 a__and :: tt:plus:isNat:s:0:U11:U21:and -> tt:plus:isNat:s:0:U11:U21:and -> tt:plus:isNat:s:0:U11:U21:and U11 :: tt:plus:isNat:s:0:U11:U21:and -> tt:plus:isNat:s:0:U11:U21:and -> tt:plus:isNat:s:0:U11:U21:and c14 :: c -> c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21 U21 :: tt:plus:isNat:s:0:U11:U21:and -> tt:plus:isNat:s:0:U11:U21:and -> tt:plus:isNat:s:0:U11:U21:and -> tt:plus:isNat:s:0:U11:U21:and c15 :: c2:c3 -> c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21 c16 :: c11:c12 -> c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21 c17 :: c11:c12 -> c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21 and :: tt:plus:isNat:s:0:U11:U21:and -> tt:plus:isNat:s:0:U11:U21:and -> tt:plus:isNat:s:0:U11:U21:and c18 :: c5 -> c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21 c19 :: c8:c9 -> c14:c15:c16:c17:c18:c19:c21 c21 :: c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21 a__U11 :: tt:plus:isNat:s:0:U11:U21:and -> tt:plus:isNat:s:0:U11:U21:and -> tt:plus:isNat:s:0:U11:U21:and a__U21 :: tt:plus:isNat:s:0:U11:U21:and -> tt:plus:isNat:s:0:U11:U21:and -> tt:plus:isNat:s:0:U11:U21:and -> tt:plus:isNat:s:0:U11:U21:and a__plus :: tt:plus:isNat:s:0:U11:U21:and -> tt:plus:isNat:s:0:U11:U21:and -> tt:plus:isNat:s:0:U11:U21:and Rewrite Strategy: INNERMOST ---------------------------------------- (39) 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_2 A__U21_3 A__AND_2 A__ISNAT_1 A__PLUS_2 MARK_1 (c) The following functions are completely defined: a__U11_2 a__U21_3 a__and_2 a__isNat_1 a__plus_2 mark_1 Due to the following rules being added: a__U11(v0, v1) -> null_a__U11 [0] a__U21(v0, v1, v2) -> null_a__U21 [0] a__and(v0, v1) -> null_a__and [0] a__isNat(v0) -> null_a__isNat [0] a__plus(v0, v1) -> null_a__plus [0] mark(v0) -> null_mark [0] And the following fresh constants: null_a__U11, null_a__U21, null_a__and, null_a__isNat, null_a__plus, null_mark, const, const1, const2, const3, const4, const5 ---------------------------------------- (40) 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) -> c(MARK(z0)) [1] A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1] A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1] A__AND(tt, z0) -> c5(MARK(z0)) [1] A__ISNAT(plus(z0, z1)) -> c8(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) [1] A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) [1] A__PLUS(z0, 0) -> c11(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) [1] A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) [1] MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) [1] MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) [1] MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) [1] MARK(isNat(z0)) -> c19(A__ISNAT(z0)) [1] MARK(s(z0)) -> c21(MARK(z0)) [1] a__U11(tt, z0) -> mark(z0) [0] a__U11(z0, z1) -> U11(z0, z1) [0] a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0] a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) [0] a__isNat(s(z0)) -> a__isNat(z0) [0] a__isNat(z0) -> isNat(z0) [0] a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) [0] a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) [0] a__plus(z0, z1) -> plus(z0, z1) [0] mark(U11(z0, z1)) -> a__U11(mark(z0), z1) [0] mark(U21(z0, z1, z2)) -> a__U21(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(isNat(z0)) -> a__isNat(z0) [0] mark(tt) -> tt [0] mark(s(z0)) -> s(mark(z0)) [0] mark(0) -> 0 [0] a__U11(v0, v1) -> null_a__U11 [0] a__U21(v0, v1, v2) -> null_a__U21 [0] a__and(v0, v1) -> null_a__and [0] a__isNat(v0) -> null_a__isNat [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:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> c tt :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark c :: c14:c15:c16:c17:c18:c19:c21 -> c MARK :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> c14:c15:c16:c17:c18:c19:c21 A__U21 :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> c2:c3 c2 :: c11:c12 -> c14:c15:c16:c17:c18:c19:c21 -> c2:c3 A__PLUS :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> c11:c12 mark :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark c3 :: c11:c12 -> c14:c15:c16:c17:c18:c19:c21 -> c2:c3 A__AND :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> c5 c5 :: c14:c15:c16:c17:c18:c19:c21 -> c5 A__ISNAT :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> c8:c9 plus :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark c8 :: c5 -> c8:c9 -> c8:c9 a__isNat :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark isNat :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark s :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark c9 :: c8:c9 -> c8:c9 0 :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark c11 :: c -> c8:c9 -> c11:c12 c12 :: c2:c3 -> c5 -> c8:c9 -> c11:c12 a__and :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark U11 :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark c14 :: c -> c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21 U21 :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark c15 :: c2:c3 -> c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21 c16 :: c11:c12 -> c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21 c17 :: c11:c12 -> c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21 and :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark c18 :: c5 -> c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21 c19 :: c8:c9 -> c14:c15:c16:c17:c18:c19:c21 c21 :: c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21 a__U11 :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark a__U21 :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark a__plus :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark null_a__U11 :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark null_a__U21 :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark null_a__and :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark null_a__isNat :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark null_a__plus :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark null_mark :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark const :: c const1 :: c14:c15:c16:c17:c18:c19:c21 const2 :: c2:c3 const3 :: c11:c12 const4 :: c5 const5 :: c8:c9 Rewrite Strategy: INNERMOST ---------------------------------------- (41) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (42) 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) -> c(MARK(z0)) [1] A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1] A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1] A__AND(tt, z0) -> c5(MARK(z0)) [1] A__ISNAT(plus(0, z1)) -> c8(A__AND(tt, isNat(z1)), A__ISNAT(0)) [1] A__ISNAT(plus(plus(z0119, z179), z1)) -> c8(A__AND(a__and(a__isNat(z0119), isNat(z179)), isNat(z1)), A__ISNAT(plus(z0119, z179))) [1] A__ISNAT(plus(s(z0120), z1)) -> c8(A__AND(a__isNat(z0120), isNat(z1)), A__ISNAT(s(z0120))) [1] A__ISNAT(plus(z0, z1)) -> c8(A__AND(isNat(z0), isNat(z1)), A__ISNAT(z0)) [1] A__ISNAT(plus(z0, z1)) -> c8(A__AND(null_a__isNat, isNat(z1)), A__ISNAT(z0)) [1] A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) [1] A__PLUS(0, 0) -> c11(A__U11(tt, 0), A__ISNAT(0)) [1] A__PLUS(plus(z0121, z180), 0) -> c11(A__U11(a__and(a__isNat(z0121), isNat(z180)), plus(z0121, z180)), A__ISNAT(plus(z0121, z180))) [1] A__PLUS(s(z0122), 0) -> c11(A__U11(a__isNat(z0122), s(z0122)), A__ISNAT(s(z0122))) [1] A__PLUS(z0, 0) -> c11(A__U11(isNat(z0), z0), A__ISNAT(z0)) [1] A__PLUS(z0, 0) -> c11(A__U11(null_a__isNat, z0), A__ISNAT(z0)) [1] A__PLUS(z0, s(0)) -> c12(A__U21(a__and(tt, isNat(z0)), 0, z0), A__AND(tt, isNat(z0)), A__ISNAT(0)) [1] A__PLUS(z0, s(0)) -> c12(A__U21(a__and(tt, isNat(z0)), 0, z0), A__AND(isNat(0), isNat(z0)), A__ISNAT(0)) [1] A__PLUS(z0, s(0)) -> c12(A__U21(a__and(tt, isNat(z0)), 0, z0), A__AND(null_a__isNat, isNat(z0)), A__ISNAT(0)) [1] A__PLUS(z0, s(plus(z0123, z181))) -> c12(A__U21(a__and(a__and(a__isNat(z0123), isNat(z181)), isNat(z0)), plus(z0123, z181), z0), A__AND(a__and(a__isNat(z0123), isNat(z181)), isNat(z0)), A__ISNAT(plus(z0123, z181))) [1] A__PLUS(z0, s(plus(z0123, z181))) -> c12(A__U21(a__and(a__and(a__isNat(z0123), isNat(z181)), isNat(z0)), plus(z0123, z181), z0), A__AND(isNat(plus(z0123, z181)), isNat(z0)), A__ISNAT(plus(z0123, z181))) [1] A__PLUS(z0, s(plus(z0123, z181))) -> c12(A__U21(a__and(a__and(a__isNat(z0123), isNat(z181)), isNat(z0)), plus(z0123, z181), z0), A__AND(null_a__isNat, isNat(z0)), A__ISNAT(plus(z0123, z181))) [1] A__PLUS(z0, s(s(z0124))) -> c12(A__U21(a__and(a__isNat(z0124), isNat(z0)), s(z0124), z0), A__AND(a__isNat(z0124), isNat(z0)), A__ISNAT(s(z0124))) [1] A__PLUS(z0, s(s(z0124))) -> c12(A__U21(a__and(a__isNat(z0124), isNat(z0)), s(z0124), z0), A__AND(isNat(s(z0124)), isNat(z0)), A__ISNAT(s(z0124))) [1] A__PLUS(z0, s(s(z0124))) -> c12(A__U21(a__and(a__isNat(z0124), isNat(z0)), s(z0124), z0), A__AND(null_a__isNat, isNat(z0)), A__ISNAT(s(z0124))) [1] A__PLUS(z0, s(0)) -> c12(A__U21(a__and(isNat(0), isNat(z0)), 0, z0), A__AND(tt, isNat(z0)), A__ISNAT(0)) [1] A__PLUS(z0, s(plus(z0125, z182))) -> c12(A__U21(a__and(isNat(plus(z0125, z182)), isNat(z0)), plus(z0125, z182), z0), A__AND(a__and(a__isNat(z0125), isNat(z182)), isNat(z0)), A__ISNAT(plus(z0125, z182))) [1] A__PLUS(z0, s(s(z0126))) -> c12(A__U21(a__and(isNat(s(z0126)), isNat(z0)), s(z0126), z0), A__AND(a__isNat(z0126), isNat(z0)), A__ISNAT(s(z0126))) [1] A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(isNat(z1), isNat(z0)), z1, z0), A__AND(isNat(z1), isNat(z0)), A__ISNAT(z1)) [1] A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(isNat(z1), isNat(z0)), z1, z0), A__AND(null_a__isNat, isNat(z0)), A__ISNAT(z1)) [1] A__PLUS(z0, s(0)) -> c12(A__U21(a__and(null_a__isNat, isNat(z0)), 0, z0), A__AND(tt, isNat(z0)), A__ISNAT(0)) [1] A__PLUS(z0, s(plus(z0127, z183))) -> c12(A__U21(a__and(null_a__isNat, isNat(z0)), plus(z0127, z183), z0), A__AND(a__and(a__isNat(z0127), isNat(z183)), isNat(z0)), A__ISNAT(plus(z0127, z183))) [1] A__PLUS(z0, s(s(z0128))) -> c12(A__U21(a__and(null_a__isNat, isNat(z0)), s(z0128), z0), A__AND(a__isNat(z0128), isNat(z0)), A__ISNAT(s(z0128))) [1] A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(null_a__isNat, isNat(z0)), z1, z0), A__AND(isNat(z1), isNat(z0)), A__ISNAT(z1)) [1] A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(null_a__isNat, isNat(z0)), z1, z0), A__AND(null_a__isNat, isNat(z0)), A__ISNAT(z1)) [1] MARK(U11(U11(z0129, z184), z1)) -> c14(A__U11(a__U11(mark(z0129), z184), z1), MARK(U11(z0129, z184))) [1] MARK(U11(U21(z0130, z185, z219), z1)) -> c14(A__U11(a__U21(mark(z0130), z185, z219), z1), MARK(U21(z0130, z185, z219))) [1] MARK(U11(plus(z0131, z186), z1)) -> c14(A__U11(a__plus(mark(z0131), mark(z186)), z1), MARK(plus(z0131, z186))) [1] MARK(U11(and(z0132, z187), z1)) -> c14(A__U11(a__and(mark(z0132), z187), z1), MARK(and(z0132, z187))) [1] MARK(U11(isNat(z0133), z1)) -> c14(A__U11(a__isNat(z0133), z1), MARK(isNat(z0133))) [1] MARK(U11(tt, z1)) -> c14(A__U11(tt, z1), MARK(tt)) [1] MARK(U11(s(z0134), z1)) -> c14(A__U11(s(mark(z0134)), z1), MARK(s(z0134))) [1] MARK(U11(0, z1)) -> c14(A__U11(0, z1), MARK(0)) [1] MARK(U11(z0, z1)) -> c14(A__U11(null_mark, z1), MARK(z0)) [1] MARK(U21(U11(z0135, z188), z1, z2)) -> c15(A__U21(a__U11(mark(z0135), z188), z1, z2), MARK(U11(z0135, z188))) [1] MARK(U21(U21(z0136, z189, z220), z1, z2)) -> c15(A__U21(a__U21(mark(z0136), z189, z220), z1, z2), MARK(U21(z0136, z189, z220))) [1] MARK(U21(plus(z0137, z190), z1, z2)) -> c15(A__U21(a__plus(mark(z0137), mark(z190)), z1, z2), MARK(plus(z0137, z190))) [1] MARK(U21(and(z0138, z191), z1, z2)) -> c15(A__U21(a__and(mark(z0138), z191), z1, z2), MARK(and(z0138, z191))) [1] MARK(U21(isNat(z0139), z1, z2)) -> c15(A__U21(a__isNat(z0139), z1, z2), MARK(isNat(z0139))) [1] MARK(U21(tt, z1, z2)) -> c15(A__U21(tt, z1, z2), MARK(tt)) [1] MARK(U21(s(z0140), z1, z2)) -> c15(A__U21(s(mark(z0140)), z1, z2), MARK(s(z0140))) [1] MARK(U21(0, z1, z2)) -> c15(A__U21(0, z1, z2), MARK(0)) [1] MARK(U21(z0, z1, z2)) -> c15(A__U21(null_mark, z1, z2), MARK(z0)) [1] MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(and(U11(z0261, z1172), z1)) -> c18(A__AND(a__U11(mark(z0261), z1172), z1), MARK(U11(z0261, z1172))) [1] MARK(and(U21(z0262, z1173, z241), z1)) -> c18(A__AND(a__U21(mark(z0262), z1173, z241), z1), MARK(U21(z0262, z1173, z241))) [1] MARK(and(plus(z0263, z1174), z1)) -> c18(A__AND(a__plus(mark(z0263), mark(z1174)), z1), MARK(plus(z0263, z1174))) [1] MARK(and(and(z0264, z1175), z1)) -> c18(A__AND(a__and(mark(z0264), z1175), z1), MARK(and(z0264, z1175))) [1] MARK(and(isNat(z0265), z1)) -> c18(A__AND(a__isNat(z0265), z1), MARK(isNat(z0265))) [1] MARK(and(tt, z1)) -> c18(A__AND(tt, z1), MARK(tt)) [1] MARK(and(s(z0266), z1)) -> c18(A__AND(s(mark(z0266)), z1), MARK(s(z0266))) [1] MARK(and(0, z1)) -> c18(A__AND(0, z1), MARK(0)) [1] MARK(and(z0, z1)) -> c18(A__AND(null_mark, z1), MARK(z0)) [1] MARK(isNat(z0)) -> c19(A__ISNAT(z0)) [1] MARK(s(z0)) -> c21(MARK(z0)) [1] a__U11(tt, z0) -> mark(z0) [0] a__U11(z0, z1) -> U11(z0, z1) [0] a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0] a__U21(z0, z1, z2) -> U21(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__and(tt, isNat(z1)) [0] a__isNat(plus(plus(z0327, z1216), z1)) -> a__and(a__and(a__isNat(z0327), isNat(z1216)), isNat(z1)) [0] a__isNat(plus(s(z0328), z1)) -> a__and(a__isNat(z0328), isNat(z1)) [0] a__isNat(plus(z0, z1)) -> a__and(isNat(z0), isNat(z1)) [0] a__isNat(plus(z0, z1)) -> a__and(null_a__isNat, isNat(z1)) [0] a__isNat(s(z0)) -> a__isNat(z0) [0] a__isNat(z0) -> isNat(z0) [0] a__plus(0, 0) -> a__U11(tt, 0) [0] a__plus(plus(z0329, z1217), 0) -> a__U11(a__and(a__isNat(z0329), isNat(z1217)), plus(z0329, z1217)) [0] a__plus(s(z0330), 0) -> a__U11(a__isNat(z0330), s(z0330)) [0] a__plus(z0, 0) -> a__U11(isNat(z0), z0) [0] a__plus(z0, 0) -> a__U11(null_a__isNat, z0) [0] a__plus(z0, s(0)) -> a__U21(a__and(tt, isNat(z0)), 0, z0) [0] a__plus(z0, s(plus(z0331, z1218))) -> a__U21(a__and(a__and(a__isNat(z0331), isNat(z1218)), isNat(z0)), plus(z0331, z1218), z0) [0] a__plus(z0, s(s(z0332))) -> a__U21(a__and(a__isNat(z0332), isNat(z0)), s(z0332), z0) [0] a__plus(z0, s(z1)) -> a__U21(a__and(isNat(z1), isNat(z0)), z1, z0) [0] a__plus(z0, s(z1)) -> a__U21(a__and(null_a__isNat, isNat(z0)), z1, z0) [0] a__plus(z0, z1) -> plus(z0, z1) [0] mark(U11(U11(z0333, z1219), z1)) -> a__U11(a__U11(mark(z0333), z1219), z1) [0] mark(U11(U21(z0334, z1220, z252), z1)) -> a__U11(a__U21(mark(z0334), z1220, z252), z1) [0] mark(U11(plus(z0335, z1221), z1)) -> a__U11(a__plus(mark(z0335), mark(z1221)), z1) [0] mark(U11(and(z0336, z1222), z1)) -> a__U11(a__and(mark(z0336), z1222), z1) [0] mark(U11(isNat(z0337), z1)) -> a__U11(a__isNat(z0337), z1) [0] mark(U11(tt, z1)) -> a__U11(tt, z1) [0] mark(U11(s(z0338), z1)) -> a__U11(s(mark(z0338)), z1) [0] mark(U11(0, z1)) -> a__U11(0, z1) [0] mark(U11(z0, z1)) -> a__U11(null_mark, z1) [0] mark(U21(U11(z0339, z1223), z1, z2)) -> a__U21(a__U11(mark(z0339), z1223), z1, z2) [0] mark(U21(U21(z0340, z1224, z253), z1, z2)) -> a__U21(a__U21(mark(z0340), z1224, z253), z1, z2) [0] mark(U21(plus(z0341, z1225), z1, z2)) -> a__U21(a__plus(mark(z0341), mark(z1225)), z1, z2) [0] mark(U21(and(z0342, z1226), z1, z2)) -> a__U21(a__and(mark(z0342), z1226), z1, z2) [0] mark(U21(isNat(z0343), z1, z2)) -> a__U21(a__isNat(z0343), z1, z2) [0] mark(U21(tt, z1, z2)) -> a__U21(tt, z1, z2) [0] mark(U21(s(z0344), z1, z2)) -> a__U21(s(mark(z0344)), z1, z2) [0] mark(U21(0, z1, z2)) -> a__U21(0, z1, z2) [0] mark(U21(z0, z1, z2)) -> a__U21(null_mark, z1, z2) [0] mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0] mark(and(U11(z0405, z1267), z1)) -> a__and(a__U11(mark(z0405), z1267), z1) [0] mark(and(U21(z0406, z1268, z264), z1)) -> a__and(a__U21(mark(z0406), z1268, z264), z1) [0] mark(and(plus(z0407, z1269), z1)) -> a__and(a__plus(mark(z0407), mark(z1269)), z1) [0] mark(and(and(z0408, z1270), z1)) -> a__and(a__and(mark(z0408), z1270), z1) [0] mark(and(isNat(z0409), z1)) -> a__and(a__isNat(z0409), z1) [0] mark(and(tt, z1)) -> a__and(tt, z1) [0] mark(and(s(z0410), z1)) -> a__and(s(mark(z0410)), z1) [0] mark(and(0, z1)) -> a__and(0, z1) [0] mark(and(z0, z1)) -> a__and(null_mark, z1) [0] mark(isNat(z0)) -> a__isNat(z0) [0] mark(tt) -> tt [0] mark(s(z0)) -> s(mark(z0)) [0] mark(0) -> 0 [0] a__U11(v0, v1) -> null_a__U11 [0] a__U21(v0, v1, v2) -> null_a__U21 [0] a__and(v0, v1) -> null_a__and [0] a__isNat(v0) -> null_a__isNat [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:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> c tt :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark c :: c14:c15:c16:c17:c18:c19:c21 -> c MARK :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> c14:c15:c16:c17:c18:c19:c21 A__U21 :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> c2:c3 c2 :: c11:c12 -> c14:c15:c16:c17:c18:c19:c21 -> c2:c3 A__PLUS :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> c11:c12 mark :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark c3 :: c11:c12 -> c14:c15:c16:c17:c18:c19:c21 -> c2:c3 A__AND :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> c5 c5 :: c14:c15:c16:c17:c18:c19:c21 -> c5 A__ISNAT :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> c8:c9 plus :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark c8 :: c5 -> c8:c9 -> c8:c9 a__isNat :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark isNat :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark s :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark c9 :: c8:c9 -> c8:c9 0 :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark c11 :: c -> c8:c9 -> c11:c12 c12 :: c2:c3 -> c5 -> c8:c9 -> c11:c12 a__and :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark U11 :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark c14 :: c -> c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21 U21 :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark c15 :: c2:c3 -> c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21 c16 :: c11:c12 -> c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21 c17 :: c11:c12 -> c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21 and :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark c18 :: c5 -> c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21 c19 :: c8:c9 -> c14:c15:c16:c17:c18:c19:c21 c21 :: c14:c15:c16:c17:c18:c19:c21 -> c14:c15:c16:c17:c18:c19:c21 a__U11 :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark a__U21 :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark a__plus :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark null_a__U11 :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark null_a__U21 :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark null_a__and :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark null_a__isNat :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark null_a__plus :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark null_mark :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark const :: c const1 :: c14:c15:c16:c17:c18:c19:c21 const2 :: c2:c3 const3 :: c11:c12 const4 :: c5 const5 :: c8:c9 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 null_a__U11 => 0 null_a__U21 => 0 null_a__and => 0 null_a__isNat => 0 null_a__plus => 0 null_mark => 0 const => 0 const1 => 0 const2 => 0 const3 => 0 const4 => 0 const5 => 0 ---------------------------------------- (44) 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__ISNAT(z0) :|: z = 1 + z0, z0 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__AND(a__isNat(z0120), 1 + z1) + A__ISNAT(1 + z0120) :|: z1 >= 0, z = 1 + (1 + z0120) + z1, z0120 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__AND(a__and(a__isNat(z0119), 1 + z179), 1 + z1) + A__ISNAT(1 + z0119 + z179) :|: z0119 >= 0, z1 >= 0, z179 >= 0, z = 1 + (1 + z0119 + z179) + z1 A__ISNAT(z) -{ 1 }-> 1 + A__AND(1, 1 + z1) + A__ISNAT(0) :|: z1 >= 0, z = 1 + 0 + z1 A__ISNAT(z) -{ 1 }-> 1 + A__AND(0, 1 + z1) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNAT(z) -{ 1 }-> 1 + A__AND(1 + z0, 1 + z1) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__PLUS(z, z') -{ 1 }-> 1 + A__U11(a__isNat(z0122), 1 + z0122) + A__ISNAT(1 + z0122) :|: z = 1 + z0122, z0122 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U11(a__and(a__isNat(z0121), 1 + z180), 1 + z0121 + z180) + A__ISNAT(1 + z0121 + z180) :|: z0121 >= 0, z180 >= 0, z = 1 + z0121 + z180, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U11(1, 0) + A__ISNAT(0) :|: z = 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U11(0, z0) + A__ISNAT(z0) :|: z = z0, z0 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U11(1 + z0, z0) + A__ISNAT(z0) :|: z = z0, z0 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(a__isNat(z0124), 1 + z0), 1 + z0124, z0) + A__AND(a__isNat(z0124), 1 + z0) + A__ISNAT(1 + z0124) :|: z = z0, z' = 1 + (1 + z0124), z0 >= 0, z0124 >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(a__isNat(z0124), 1 + z0), 1 + z0124, z0) + A__AND(0, 1 + z0) + A__ISNAT(1 + z0124) :|: z = z0, z' = 1 + (1 + z0124), z0 >= 0, z0124 >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(a__isNat(z0124), 1 + z0), 1 + z0124, z0) + A__AND(1 + (1 + z0124), 1 + z0) + A__ISNAT(1 + z0124) :|: z = z0, z' = 1 + (1 + z0124), z0 >= 0, z0124 >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(a__and(a__isNat(z0123), 1 + z181), 1 + z0), 1 + z0123 + z181, z0) + A__AND(a__and(a__isNat(z0123), 1 + z181), 1 + z0) + A__ISNAT(1 + z0123 + z181) :|: z = z0, z' = 1 + (1 + z0123 + z181), z181 >= 0, z0 >= 0, z0123 >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(a__and(a__isNat(z0123), 1 + z181), 1 + z0), 1 + z0123 + z181, z0) + A__AND(0, 1 + z0) + A__ISNAT(1 + z0123 + z181) :|: z = z0, z' = 1 + (1 + z0123 + z181), z181 >= 0, z0 >= 0, z0123 >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(a__and(a__isNat(z0123), 1 + z181), 1 + z0), 1 + z0123 + z181, z0) + A__AND(1 + (1 + z0123 + z181), 1 + z0) + A__ISNAT(1 + z0123 + z181) :|: z = z0, z' = 1 + (1 + z0123 + z181), z181 >= 0, z0 >= 0, z0123 >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(1, 1 + z0), 0, z0) + A__AND(1, 1 + z0) + A__ISNAT(0) :|: z = z0, z' = 1 + 0, z0 >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(1, 1 + z0), 0, z0) + A__AND(0, 1 + z0) + A__ISNAT(0) :|: z = z0, z' = 1 + 0, z0 >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(1, 1 + z0), 0, z0) + A__AND(1 + 0, 1 + z0) + A__ISNAT(0) :|: z = z0, z' = 1 + 0, z0 >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(0, 1 + z0), z1, z0) + A__AND(0, 1 + z0) + A__ISNAT(z1) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(0, 1 + z0), z1, z0) + A__AND(1 + z1, 1 + z0) + A__ISNAT(z1) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(0, 1 + z0), 0, z0) + A__AND(1, 1 + z0) + A__ISNAT(0) :|: z = z0, z' = 1 + 0, z0 >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(0, 1 + z0), 1 + z0128, z0) + A__AND(a__isNat(z0128), 1 + z0) + A__ISNAT(1 + z0128) :|: z = z0, z' = 1 + (1 + z0128), z0 >= 0, z0128 >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(0, 1 + z0), 1 + z0127 + z183, z0) + A__AND(a__and(a__isNat(z0127), 1 + z183), 1 + z0) + A__ISNAT(1 + z0127 + z183) :|: z183 >= 0, z = z0, z0 >= 0, z0127 >= 0, z' = 1 + (1 + z0127 + z183) A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(1 + z1, 1 + z0), z1, z0) + A__AND(0, 1 + z0) + A__ISNAT(z1) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(1 + z1, 1 + z0), z1, z0) + A__AND(1 + z1, 1 + z0) + A__ISNAT(z1) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(1 + 0, 1 + z0), 0, z0) + A__AND(1, 1 + z0) + A__ISNAT(0) :|: z = z0, z' = 1 + 0, z0 >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(1 + (1 + z0126), 1 + z0), 1 + z0126, z0) + A__AND(a__isNat(z0126), 1 + z0) + A__ISNAT(1 + z0126) :|: z' = 1 + (1 + z0126), z = z0, z0 >= 0, z0126 >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(1 + (1 + z0125 + z182), 1 + z0), 1 + z0125 + z182, z0) + A__AND(a__and(a__isNat(z0125), 1 + z182), 1 + z0) + A__ISNAT(1 + z0125 + z182) :|: z = z0, z' = 1 + (1 + z0125 + z182), z182 >= 0, z0 >= 0, z0125 >= 0 A__U11(z, z') -{ 1 }-> 1 + MARK(z0) :|: z = 1, z0 >= 0, z' = z0 A__U21(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z1), mark(z0)) + MARK(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U21(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__ISNAT(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__plus(mark(z0137), mark(z190)), z1, z2) + MARK(1 + z0137 + z190) :|: z1 >= 0, z190 >= 0, z = 1 + (1 + z0137 + z190) + z1 + z2, z0137 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__isNat(z0139), z1, z2) + MARK(1 + z0139) :|: z = 1 + (1 + z0139) + z1 + z2, z1 >= 0, z0139 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__and(mark(z0138), z191), z1, z2) + MARK(1 + z0138 + z191) :|: z = 1 + (1 + z0138 + z191) + z1 + z2, z1 >= 0, z0138 >= 0, z191 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U21(mark(z0136), z189, z220), z1, z2) + MARK(1 + z0136 + z189 + z220) :|: z0136 >= 0, z1 >= 0, z = 1 + (1 + z0136 + z189 + z220) + z1 + z2, z220 >= 0, z189 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U11(mark(z0135), z188), z1, z2) + MARK(1 + z0135 + z188) :|: z1 >= 0, z188 >= 0, z0135 >= 0, z = 1 + (1 + z0135 + z188) + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(1, z1, z2) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(0, z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(0, z1, z2) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(1 + mark(z0140), z1, z2) + MARK(1 + z0140) :|: z1 >= 0, z = 1 + (1 + z0140) + z1 + z2, z0140 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__plus(mark(z0131), mark(z186)), z1) + MARK(1 + z0131 + z186) :|: z1 >= 0, z0131 >= 0, z = 1 + (1 + z0131 + z186) + z1, z186 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__isNat(z0133), z1) + MARK(1 + z0133) :|: z1 >= 0, z0133 >= 0, z = 1 + (1 + z0133) + z1 MARK(z) -{ 1 }-> 1 + A__U11(a__and(mark(z0132), z187), z1) + MARK(1 + z0132 + z187) :|: z0132 >= 0, z187 >= 0, z1 >= 0, z = 1 + (1 + z0132 + z187) + z1 MARK(z) -{ 1 }-> 1 + A__U11(a__U21(mark(z0130), z185, z219), z1) + MARK(1 + z0130 + z185 + z219) :|: z = 1 + (1 + z0130 + z185 + z219) + z1, z1 >= 0, z219 >= 0, z0130 >= 0, z185 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U11(mark(z0129), z184), z1) + MARK(1 + z0129 + z184) :|: z1 >= 0, z0129 >= 0, z184 >= 0, z = 1 + (1 + z0129 + z184) + z1 MARK(z) -{ 1 }-> 1 + A__U11(1, z1) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 MARK(z) -{ 1 }-> 1 + A__U11(0, z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U11(0, z1) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 MARK(z) -{ 1 }-> 1 + A__U11(1 + mark(z0134), z1) + MARK(1 + z0134) :|: z1 >= 0, z0134 >= 0, z = 1 + (1 + z0134) + z1 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(z0263), mark(z1174)), z1) + MARK(1 + z0263 + z1174) :|: z0263 >= 0, z1 >= 0, z1174 >= 0, z = 1 + (1 + z0263 + z1174) + z1 MARK(z) -{ 1 }-> 1 + A__AND(a__isNat(z0265), z1) + MARK(1 + z0265) :|: z1 >= 0, z = 1 + (1 + z0265) + z1, z0265 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__and(mark(z0264), z1175), z1) + MARK(1 + z0264 + z1175) :|: z1 >= 0, z1175 >= 0, z = 1 + (1 + z0264 + z1175) + z1, z0264 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__U21(mark(z0262), z1173, z241), z1) + MARK(1 + z0262 + z1173 + z241) :|: z0262 >= 0, z1 >= 0, z1173 >= 0, z = 1 + (1 + z0262 + z1173 + z241) + z1, z241 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__U11(mark(z0261), z1172), z1) + MARK(1 + z0261 + z1172) :|: z1172 >= 0, z1 >= 0, z0261 >= 0, z = 1 + (1 + z0261 + z1172) + z1 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(z0266), z1) + MARK(1 + z0266) :|: z1 >= 0, z0266 >= 0, z = 1 + (1 + z0266) + z1 a__U11(z, z') -{ 0 }-> mark(z0) :|: z = 1, z0 >= 0, z' = z0 a__U11(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U11(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U21(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U21(z, z', z'') -{ 0 }-> 1 + a__plus(mark(z1), mark(z0)) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U21(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__isNat(z0) :|: z = 1 + z0, z0 >= 0 a__isNat(z) -{ 0 }-> a__and(a__isNat(z0328), 1 + z1) :|: z1 >= 0, z0328 >= 0, z = 1 + (1 + z0328) + z1 a__isNat(z) -{ 0 }-> a__and(a__and(a__isNat(z0327), 1 + z1216), 1 + z1) :|: z1216 >= 0, z1 >= 0, z = 1 + (1 + z0327 + z1216) + z1, z0327 >= 0 a__isNat(z) -{ 0 }-> a__and(1, 1 + z1) :|: z1 >= 0, z = 1 + 0 + z1 a__isNat(z) -{ 0 }-> a__and(0, 1 + z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNat(z) -{ 0 }-> a__and(1 + z0, 1 + 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__plus(z, z') -{ 0 }-> a__U21(a__and(a__isNat(z0332), 1 + z0), 1 + z0332, z0) :|: z = z0, z' = 1 + (1 + z0332), z0332 >= 0, z0 >= 0 a__plus(z, z') -{ 0 }-> a__U21(a__and(a__and(a__isNat(z0331), 1 + z1218), 1 + z0), 1 + z0331 + z1218, z0) :|: z = z0, z' = 1 + (1 + z0331 + z1218), z0331 >= 0, z1218 >= 0, z0 >= 0 a__plus(z, z') -{ 0 }-> a__U21(a__and(1, 1 + z0), 0, z0) :|: z = z0, z' = 1 + 0, z0 >= 0 a__plus(z, z') -{ 0 }-> a__U21(a__and(0, 1 + z0), z1, z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 a__plus(z, z') -{ 0 }-> a__U21(a__and(1 + z1, 1 + z0), z1, z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 a__plus(z, z') -{ 0 }-> a__U11(a__isNat(z0330), 1 + z0330) :|: z0330 >= 0, z = 1 + z0330, z' = 0 a__plus(z, z') -{ 0 }-> a__U11(a__and(a__isNat(z0329), 1 + z1217), 1 + z0329 + z1217) :|: z = 1 + z0329 + z1217, z0329 >= 0, z1217 >= 0, z' = 0 a__plus(z, z') -{ 0 }-> a__U11(1, 0) :|: z = 0, z' = 0 a__plus(z, z') -{ 0 }-> a__U11(0, z0) :|: z = z0, z0 >= 0, z' = 0 a__plus(z, z') -{ 0 }-> a__U11(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__isNat(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__and(a__plus(mark(z0407), mark(z1269)), z1) :|: z1 >= 0, z1269 >= 0, z = 1 + (1 + z0407 + z1269) + z1, z0407 >= 0 mark(z) -{ 0 }-> a__and(a__isNat(z0409), z1) :|: z0409 >= 0, z1 >= 0, z = 1 + (1 + z0409) + z1 mark(z) -{ 0 }-> a__and(a__and(mark(z0408), z1270), z1) :|: z1 >= 0, z0408 >= 0, z1270 >= 0, z = 1 + (1 + z0408 + z1270) + z1 mark(z) -{ 0 }-> a__and(a__U21(mark(z0406), z1268, z264), z1) :|: z1268 >= 0, z1 >= 0, z0406 >= 0, z = 1 + (1 + z0406 + z1268 + z264) + z1, z264 >= 0 mark(z) -{ 0 }-> a__and(a__U11(mark(z0405), z1267), z1) :|: z0405 >= 0, z1 >= 0, z = 1 + (1 + z0405 + z1267) + z1, z1267 >= 0 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(z0410), z1) :|: z1 >= 0, z0410 >= 0, z = 1 + (1 + z0410) + z1 mark(z) -{ 0 }-> a__U21(a__plus(mark(z0341), mark(z1225)), z1, z2) :|: z0341 >= 0, z1 >= 0, z1225 >= 0, z2 >= 0, z = 1 + (1 + z0341 + z1225) + z1 + z2 mark(z) -{ 0 }-> a__U21(a__isNat(z0343), z1, z2) :|: z1 >= 0, z = 1 + (1 + z0343) + z1 + z2, z2 >= 0, z0343 >= 0 mark(z) -{ 0 }-> a__U21(a__and(mark(z0342), z1226), z1, z2) :|: z = 1 + (1 + z0342 + z1226) + z1 + z2, z1226 >= 0, z1 >= 0, z0342 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U21(a__U21(mark(z0340), z1224, z253), z1, z2) :|: z1 >= 0, z = 1 + (1 + z0340 + z1224 + z253) + z1 + z2, z0340 >= 0, z1224 >= 0, z253 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U21(a__U11(mark(z0339), z1223), z1, z2) :|: z1 >= 0, z1223 >= 0, z0339 >= 0, z = 1 + (1 + z0339 + z1223) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U21(1, z1, z2) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U21(0, z1, z2) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U21(0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U21(1 + mark(z0344), z1, z2) :|: z0344 >= 0, z1 >= 0, z = 1 + (1 + z0344) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U11(a__plus(mark(z0335), mark(z1221)), z1) :|: z1 >= 0, z = 1 + (1 + z0335 + z1221) + z1, z1221 >= 0, z0335 >= 0 mark(z) -{ 0 }-> a__U11(a__isNat(z0337), z1) :|: z = 1 + (1 + z0337) + z1, z1 >= 0, z0337 >= 0 mark(z) -{ 0 }-> a__U11(a__and(mark(z0336), z1222), z1) :|: z1222 >= 0, z1 >= 0, z = 1 + (1 + z0336 + z1222) + z1, z0336 >= 0 mark(z) -{ 0 }-> a__U11(a__U21(mark(z0334), z1220, z252), z1) :|: z0334 >= 0, z1 >= 0, z252 >= 0, z = 1 + (1 + z0334 + z1220 + z252) + z1, z1220 >= 0 mark(z) -{ 0 }-> a__U11(a__U11(mark(z0333), z1219), z1) :|: z1 >= 0, z = 1 + (1 + z0333 + z1219) + z1, z1219 >= 0, z0333 >= 0 mark(z) -{ 0 }-> a__U11(1, z1) :|: z1 >= 0, z = 1 + 1 + z1 mark(z) -{ 0 }-> a__U11(0, z1) :|: z1 >= 0, z = 1 + 0 + z1 mark(z) -{ 0 }-> a__U11(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U11(1 + mark(z0338), z1) :|: z0338 >= 0, z1 >= 0, z = 1 + (1 + z0338) + z1 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 ---------------------------------------- (45) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (46) 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__ISNAT(z - 1) :|: z - 1 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__AND(a__isNat(z0120), 1 + z1) + A__ISNAT(1 + z0120) :|: z1 >= 0, z = 1 + (1 + z0120) + z1, z0120 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__AND(a__and(a__isNat(z0119), 1 + z179), 1 + z1) + A__ISNAT(1 + z0119 + z179) :|: z0119 >= 0, z1 >= 0, z179 >= 0, z = 1 + (1 + z0119 + z179) + z1 A__ISNAT(z) -{ 1 }-> 1 + A__AND(1, 1 + (z - 1)) + A__ISNAT(0) :|: z - 1 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__AND(0, 1 + z1) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNAT(z) -{ 1 }-> 1 + A__AND(1 + z0, 1 + z1) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__PLUS(z, z') -{ 1 }-> 1 + A__U11(a__isNat(z - 1), 1 + (z - 1)) + A__ISNAT(1 + (z - 1)) :|: z - 1 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U11(a__and(a__isNat(z0121), 1 + z180), 1 + z0121 + z180) + A__ISNAT(1 + z0121 + z180) :|: z0121 >= 0, z180 >= 0, z = 1 + z0121 + z180, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U11(1, 0) + A__ISNAT(0) :|: z = 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U11(0, z) + A__ISNAT(z) :|: z >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U11(1 + z, z) + A__ISNAT(z) :|: z >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(a__isNat(z' - 2), 1 + z), 1 + (z' - 2), z) + A__AND(a__isNat(z' - 2), 1 + z) + A__ISNAT(1 + (z' - 2)) :|: z >= 0, z' - 2 >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(a__isNat(z' - 2), 1 + z), 1 + (z' - 2), z) + A__AND(0, 1 + z) + A__ISNAT(1 + (z' - 2)) :|: z >= 0, z' - 2 >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(a__isNat(z' - 2), 1 + z), 1 + (z' - 2), z) + A__AND(1 + (1 + (z' - 2)), 1 + z) + A__ISNAT(1 + (z' - 2)) :|: z >= 0, z' - 2 >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(a__and(a__isNat(z0123), 1 + z181), 1 + z), 1 + z0123 + z181, z) + A__AND(a__and(a__isNat(z0123), 1 + z181), 1 + z) + A__ISNAT(1 + z0123 + z181) :|: z' = 1 + (1 + z0123 + z181), z181 >= 0, z >= 0, z0123 >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(a__and(a__isNat(z0123), 1 + z181), 1 + z), 1 + z0123 + z181, z) + A__AND(0, 1 + z) + A__ISNAT(1 + z0123 + z181) :|: z' = 1 + (1 + z0123 + z181), z181 >= 0, z >= 0, z0123 >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(a__and(a__isNat(z0123), 1 + z181), 1 + z), 1 + z0123 + z181, z) + A__AND(1 + (1 + z0123 + z181), 1 + z) + A__ISNAT(1 + z0123 + z181) :|: z' = 1 + (1 + z0123 + z181), z181 >= 0, z >= 0, z0123 >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(1, 1 + z), 0, z) + A__AND(1, 1 + z) + A__ISNAT(0) :|: z' = 1 + 0, z >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(1, 1 + z), 0, z) + A__AND(0, 1 + z) + A__ISNAT(0) :|: z' = 1 + 0, z >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(1, 1 + z), 0, z) + A__AND(1 + 0, 1 + z) + A__ISNAT(0) :|: z' = 1 + 0, z >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(0, 1 + z), 0, z) + A__AND(1, 1 + z) + A__ISNAT(0) :|: z' = 1 + 0, z >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(0, 1 + z), z' - 1, z) + A__AND(0, 1 + z) + A__ISNAT(z' - 1) :|: z' - 1 >= 0, z >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(0, 1 + z), z' - 1, z) + A__AND(1 + (z' - 1), 1 + z) + A__ISNAT(z' - 1) :|: z' - 1 >= 0, z >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(0, 1 + z), 1 + (z' - 2), z) + A__AND(a__isNat(z' - 2), 1 + z) + A__ISNAT(1 + (z' - 2)) :|: z >= 0, z' - 2 >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(0, 1 + z), 1 + z0127 + z183, z) + A__AND(a__and(a__isNat(z0127), 1 + z183), 1 + z) + A__ISNAT(1 + z0127 + z183) :|: z183 >= 0, z >= 0, z0127 >= 0, z' = 1 + (1 + z0127 + z183) A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(1 + 0, 1 + z), 0, z) + A__AND(1, 1 + z) + A__ISNAT(0) :|: z' = 1 + 0, z >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(1 + (z' - 1), 1 + z), z' - 1, z) + A__AND(0, 1 + z) + A__ISNAT(z' - 1) :|: z' - 1 >= 0, z >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(1 + (z' - 1), 1 + z), z' - 1, z) + A__AND(1 + (z' - 1), 1 + z) + A__ISNAT(z' - 1) :|: z' - 1 >= 0, z >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(1 + (1 + (z' - 2)), 1 + z), 1 + (z' - 2), z) + A__AND(a__isNat(z' - 2), 1 + z) + A__ISNAT(1 + (z' - 2)) :|: z >= 0, z' - 2 >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(1 + (1 + z0125 + z182), 1 + z), 1 + z0125 + z182, z) + A__AND(a__and(a__isNat(z0125), 1 + z182), 1 + z) + A__ISNAT(1 + z0125 + z182) :|: z' = 1 + (1 + z0125 + z182), z182 >= 0, z >= 0, z0125 >= 0 A__U11(z, z') -{ 1 }-> 1 + MARK(z') :|: z = 1, z' >= 0 A__U21(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z''), mark(z')) + MARK(z') :|: z'' >= 0, z = 1, z' >= 0 A__U21(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__ISNAT(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__plus(mark(z0137), mark(z190)), z1, z2) + MARK(1 + z0137 + z190) :|: z1 >= 0, z190 >= 0, z = 1 + (1 + z0137 + z190) + z1 + z2, z0137 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__isNat(z0139), z1, z2) + MARK(1 + z0139) :|: z = 1 + (1 + z0139) + z1 + z2, z1 >= 0, z0139 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__and(mark(z0138), z191), z1, z2) + MARK(1 + z0138 + z191) :|: z = 1 + (1 + z0138 + z191) + z1 + z2, z1 >= 0, z0138 >= 0, z191 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U21(mark(z0136), z189, z220), z1, z2) + MARK(1 + z0136 + z189 + z220) :|: z0136 >= 0, z1 >= 0, z = 1 + (1 + z0136 + z189 + z220) + z1 + z2, z220 >= 0, z189 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(a__U11(mark(z0135), z188), z1, z2) + MARK(1 + z0135 + z188) :|: z1 >= 0, z188 >= 0, z0135 >= 0, z = 1 + (1 + z0135 + z188) + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(1, z1, z2) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(0, z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(0, z1, z2) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(1 + mark(z0140), z1, z2) + MARK(1 + z0140) :|: z1 >= 0, z = 1 + (1 + z0140) + z1 + z2, z0140 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__plus(mark(z0131), mark(z186)), z1) + MARK(1 + z0131 + z186) :|: z1 >= 0, z0131 >= 0, z = 1 + (1 + z0131 + z186) + z1, z186 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__isNat(z0133), z1) + MARK(1 + z0133) :|: z1 >= 0, z0133 >= 0, z = 1 + (1 + z0133) + z1 MARK(z) -{ 1 }-> 1 + A__U11(a__and(mark(z0132), z187), z1) + MARK(1 + z0132 + z187) :|: z0132 >= 0, z187 >= 0, z1 >= 0, z = 1 + (1 + z0132 + z187) + z1 MARK(z) -{ 1 }-> 1 + A__U11(a__U21(mark(z0130), z185, z219), z1) + MARK(1 + z0130 + z185 + z219) :|: z = 1 + (1 + z0130 + z185 + z219) + z1, z1 >= 0, z219 >= 0, z0130 >= 0, z185 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(a__U11(mark(z0129), z184), z1) + MARK(1 + z0129 + z184) :|: z1 >= 0, z0129 >= 0, z184 >= 0, z = 1 + (1 + z0129 + z184) + z1 MARK(z) -{ 1 }-> 1 + A__U11(1, z - 2) + MARK(1) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(0, z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U11(0, z - 1) + MARK(0) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(1 + mark(z0134), z1) + MARK(1 + z0134) :|: z1 >= 0, z0134 >= 0, z = 1 + (1 + z0134) + z1 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(z0263), mark(z1174)), z1) + MARK(1 + z0263 + z1174) :|: z0263 >= 0, z1 >= 0, z1174 >= 0, z = 1 + (1 + z0263 + z1174) + z1 MARK(z) -{ 1 }-> 1 + A__AND(a__isNat(z0265), z1) + MARK(1 + z0265) :|: z1 >= 0, z = 1 + (1 + z0265) + z1, z0265 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__and(mark(z0264), z1175), z1) + MARK(1 + z0264 + z1175) :|: z1 >= 0, z1175 >= 0, z = 1 + (1 + z0264 + z1175) + z1, z0264 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__U21(mark(z0262), z1173, z241), z1) + MARK(1 + z0262 + z1173 + z241) :|: z0262 >= 0, z1 >= 0, z1173 >= 0, z = 1 + (1 + z0262 + z1173 + z241) + z1, z241 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__U11(mark(z0261), z1172), z1) + MARK(1 + z0261 + z1172) :|: z1172 >= 0, z1 >= 0, z0261 >= 0, z = 1 + (1 + z0261 + z1172) + z1 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(z0266), z1) + MARK(1 + z0266) :|: z1 >= 0, z0266 >= 0, z = 1 + (1 + z0266) + z1 a__U11(z, z') -{ 0 }-> mark(z') :|: z = 1, z' >= 0 a__U11(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__U11(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__U21(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0 a__U21(z, z', z'') -{ 0 }-> 1 + a__plus(mark(z''), mark(z')) :|: z'' >= 0, z = 1, z' >= 0 a__U21(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__isNat(z - 1) :|: z - 1 >= 0 a__isNat(z) -{ 0 }-> a__and(a__isNat(z0328), 1 + z1) :|: z1 >= 0, z0328 >= 0, z = 1 + (1 + z0328) + z1 a__isNat(z) -{ 0 }-> a__and(a__and(a__isNat(z0327), 1 + z1216), 1 + z1) :|: z1216 >= 0, z1 >= 0, z = 1 + (1 + z0327 + z1216) + z1, z0327 >= 0 a__isNat(z) -{ 0 }-> a__and(1, 1 + (z - 1)) :|: z - 1 >= 0 a__isNat(z) -{ 0 }-> a__and(0, 1 + z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNat(z) -{ 0 }-> a__and(1 + z0, 1 + 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__plus(z, z') -{ 0 }-> a__U21(a__and(a__isNat(z' - 2), 1 + z), 1 + (z' - 2), z) :|: z' - 2 >= 0, z >= 0 a__plus(z, z') -{ 0 }-> a__U21(a__and(a__and(a__isNat(z0331), 1 + z1218), 1 + z), 1 + z0331 + z1218, z) :|: z' = 1 + (1 + z0331 + z1218), z0331 >= 0, z1218 >= 0, z >= 0 a__plus(z, z') -{ 0 }-> a__U21(a__and(1, 1 + z), 0, z) :|: z' = 1 + 0, z >= 0 a__plus(z, z') -{ 0 }-> a__U21(a__and(0, 1 + z), z' - 1, z) :|: z' - 1 >= 0, z >= 0 a__plus(z, z') -{ 0 }-> a__U21(a__and(1 + (z' - 1), 1 + z), z' - 1, z) :|: z' - 1 >= 0, z >= 0 a__plus(z, z') -{ 0 }-> a__U11(a__isNat(z - 1), 1 + (z - 1)) :|: z - 1 >= 0, z' = 0 a__plus(z, z') -{ 0 }-> a__U11(a__and(a__isNat(z0329), 1 + z1217), 1 + z0329 + z1217) :|: z = 1 + z0329 + z1217, z0329 >= 0, z1217 >= 0, z' = 0 a__plus(z, z') -{ 0 }-> a__U11(1, 0) :|: z = 0, z' = 0 a__plus(z, z') -{ 0 }-> a__U11(0, z) :|: z >= 0, z' = 0 a__plus(z, z') -{ 0 }-> a__U11(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__isNat(z - 1) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__and(a__plus(mark(z0407), mark(z1269)), z1) :|: z1 >= 0, z1269 >= 0, z = 1 + (1 + z0407 + z1269) + z1, z0407 >= 0 mark(z) -{ 0 }-> a__and(a__isNat(z0409), z1) :|: z0409 >= 0, z1 >= 0, z = 1 + (1 + z0409) + z1 mark(z) -{ 0 }-> a__and(a__and(mark(z0408), z1270), z1) :|: z1 >= 0, z0408 >= 0, z1270 >= 0, z = 1 + (1 + z0408 + z1270) + z1 mark(z) -{ 0 }-> a__and(a__U21(mark(z0406), z1268, z264), z1) :|: z1268 >= 0, z1 >= 0, z0406 >= 0, z = 1 + (1 + z0406 + z1268 + z264) + z1, z264 >= 0 mark(z) -{ 0 }-> a__and(a__U11(mark(z0405), z1267), z1) :|: z0405 >= 0, z1 >= 0, z = 1 + (1 + z0405 + z1267) + z1, z1267 >= 0 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(z0410), z1) :|: z1 >= 0, z0410 >= 0, z = 1 + (1 + z0410) + z1 mark(z) -{ 0 }-> a__U21(a__plus(mark(z0341), mark(z1225)), z1, z2) :|: z0341 >= 0, z1 >= 0, z1225 >= 0, z2 >= 0, z = 1 + (1 + z0341 + z1225) + z1 + z2 mark(z) -{ 0 }-> a__U21(a__isNat(z0343), z1, z2) :|: z1 >= 0, z = 1 + (1 + z0343) + z1 + z2, z2 >= 0, z0343 >= 0 mark(z) -{ 0 }-> a__U21(a__and(mark(z0342), z1226), z1, z2) :|: z = 1 + (1 + z0342 + z1226) + z1 + z2, z1226 >= 0, z1 >= 0, z0342 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U21(a__U21(mark(z0340), z1224, z253), z1, z2) :|: z1 >= 0, z = 1 + (1 + z0340 + z1224 + z253) + z1 + z2, z0340 >= 0, z1224 >= 0, z253 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U21(a__U11(mark(z0339), z1223), z1, z2) :|: z1 >= 0, z1223 >= 0, z0339 >= 0, z = 1 + (1 + z0339 + z1223) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U21(1, z1, z2) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U21(0, z1, z2) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U21(0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U21(1 + mark(z0344), z1, z2) :|: z0344 >= 0, z1 >= 0, z = 1 + (1 + z0344) + z1 + z2, z2 >= 0 mark(z) -{ 0 }-> a__U11(a__plus(mark(z0335), mark(z1221)), z1) :|: z1 >= 0, z = 1 + (1 + z0335 + z1221) + z1, z1221 >= 0, z0335 >= 0 mark(z) -{ 0 }-> a__U11(a__isNat(z0337), z1) :|: z = 1 + (1 + z0337) + z1, z1 >= 0, z0337 >= 0 mark(z) -{ 0 }-> a__U11(a__and(mark(z0336), z1222), z1) :|: z1222 >= 0, z1 >= 0, z = 1 + (1 + z0336 + z1222) + z1, z0336 >= 0 mark(z) -{ 0 }-> a__U11(a__U21(mark(z0334), z1220, z252), z1) :|: z0334 >= 0, z1 >= 0, z252 >= 0, z = 1 + (1 + z0334 + z1220 + z252) + z1, z1220 >= 0 mark(z) -{ 0 }-> a__U11(a__U11(mark(z0333), z1219), z1) :|: z1 >= 0, z = 1 + (1 + z0333 + z1219) + z1, z1219 >= 0, z0333 >= 0 mark(z) -{ 0 }-> a__U11(1, z - 2) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__U11(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U11(0, z - 1) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__U11(1 + mark(z0338), z1) :|: z0338 >= 0, z1 >= 0, z = 1 + (1 + z0338) + z1 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: z >= 0 mark(z) -{ 0 }-> 1 + mark(z - 1) :|: z - 1 >= 0 ---------------------------------------- (47) 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) -> null_a__U11 [0] a__U21(v0, v1, v2) -> null_a__U21 [0] a__and(v0, v1) -> null_a__and [0] a__isNat(v0) -> null_a__isNat [0] a__plus(v0, v1) -> null_a__plus [0] mark(v0) -> null_mark [0] A__U11(v0, v1) -> null_A__U11 [0] A__U21(v0, v1, v2) -> null_A__U21 [0] A__AND(v0, v1) -> null_A__AND [0] A__ISNAT(v0) -> null_A__ISNAT [0] A__PLUS(v0, v1) -> null_A__PLUS [0] MARK(v0) -> null_MARK [0] And the following fresh constants: null_a__U11, null_a__U21, null_a__and, null_a__isNat, null_a__plus, null_mark, null_A__U11, null_A__U21, null_A__AND, null_A__ISNAT, null_A__PLUS, null_MARK ---------------------------------------- (48) 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) -> c(MARK(z0)) [1] A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1] A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1] A__AND(tt, z0) -> c5(MARK(z0)) [1] A__ISNAT(plus(z0, z1)) -> c8(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) [1] A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) [1] A__PLUS(z0, 0) -> c11(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) [1] A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) [1] MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) [1] MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) [1] MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) [1] MARK(isNat(z0)) -> c19(A__ISNAT(z0)) [1] MARK(s(z0)) -> c21(MARK(z0)) [1] a__U11(tt, z0) -> mark(z0) [0] a__U11(z0, z1) -> U11(z0, z1) [0] a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0] a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) [0] a__isNat(s(z0)) -> a__isNat(z0) [0] a__isNat(z0) -> isNat(z0) [0] a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) [0] a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) [0] a__plus(z0, z1) -> plus(z0, z1) [0] mark(U11(z0, z1)) -> a__U11(mark(z0), z1) [0] mark(U21(z0, z1, z2)) -> a__U21(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(isNat(z0)) -> a__isNat(z0) [0] mark(tt) -> tt [0] mark(s(z0)) -> s(mark(z0)) [0] mark(0) -> 0 [0] a__U11(v0, v1) -> null_a__U11 [0] a__U21(v0, v1, v2) -> null_a__U21 [0] a__and(v0, v1) -> null_a__and [0] a__isNat(v0) -> null_a__isNat [0] a__plus(v0, v1) -> null_a__plus [0] mark(v0) -> null_mark [0] A__U11(v0, v1) -> null_A__U11 [0] A__U21(v0, v1, v2) -> null_A__U21 [0] A__AND(v0, v1) -> null_A__AND [0] A__ISNAT(v0) -> null_A__ISNAT [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:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> c:null_A__U11 tt :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark c :: c14:c15:c16:c17:c18:c19:c21:null_MARK -> c:null_A__U11 MARK :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> c14:c15:c16:c17:c18:c19:c21:null_MARK A__U21 :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> c2:c3:null_A__U21 c2 :: c11:c12:null_A__PLUS -> c14:c15:c16:c17:c18:c19:c21:null_MARK -> c2:c3:null_A__U21 A__PLUS :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> c11:c12:null_A__PLUS mark :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark c3 :: c11:c12:null_A__PLUS -> c14:c15:c16:c17:c18:c19:c21:null_MARK -> c2:c3:null_A__U21 A__AND :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> c5:null_A__AND c5 :: c14:c15:c16:c17:c18:c19:c21:null_MARK -> c5:null_A__AND A__ISNAT :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> c8:c9:null_A__ISNAT plus :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark c8 :: c5:null_A__AND -> c8:c9:null_A__ISNAT -> c8:c9:null_A__ISNAT a__isNat :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark isNat :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark s :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark c9 :: c8:c9:null_A__ISNAT -> c8:c9:null_A__ISNAT 0 :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark c11 :: c:null_A__U11 -> c8:c9:null_A__ISNAT -> c11:c12:null_A__PLUS c12 :: c2:c3:null_A__U21 -> c5:null_A__AND -> c8:c9:null_A__ISNAT -> c11:c12:null_A__PLUS a__and :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark U11 :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark c14 :: c:null_A__U11 -> c14:c15:c16:c17:c18:c19:c21:null_MARK -> c14:c15:c16:c17:c18:c19:c21:null_MARK U21 :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark c15 :: c2:c3:null_A__U21 -> c14:c15:c16:c17:c18:c19:c21:null_MARK -> c14:c15:c16:c17:c18:c19:c21:null_MARK c16 :: c11:c12:null_A__PLUS -> c14:c15:c16:c17:c18:c19:c21:null_MARK -> c14:c15:c16:c17:c18:c19:c21:null_MARK c17 :: c11:c12:null_A__PLUS -> c14:c15:c16:c17:c18:c19:c21:null_MARK -> c14:c15:c16:c17:c18:c19:c21:null_MARK and :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark c18 :: c5:null_A__AND -> c14:c15:c16:c17:c18:c19:c21:null_MARK -> c14:c15:c16:c17:c18:c19:c21:null_MARK c19 :: c8:c9:null_A__ISNAT -> c14:c15:c16:c17:c18:c19:c21:null_MARK c21 :: c14:c15:c16:c17:c18:c19:c21:null_MARK -> c14:c15:c16:c17:c18:c19:c21:null_MARK a__U11 :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark a__U21 :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark a__plus :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark -> tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark null_a__U11 :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark null_a__U21 :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark null_a__and :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark null_a__isNat :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark null_a__plus :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark null_mark :: tt:plus:isNat:s:0:U11:U21:and:null_a__U11:null_a__U21:null_a__and:null_a__isNat:null_a__plus:null_mark null_A__U11 :: c:null_A__U11 null_A__U21 :: c2:c3:null_A__U21 null_A__AND :: c5:null_A__AND null_A__ISNAT :: c8:c9:null_A__ISNAT null_A__PLUS :: c11:c12:null_A__PLUS null_MARK :: c14:c15:c16:c17:c18:c19:c21:null_MARK Rewrite Strategy: INNERMOST ---------------------------------------- (49) 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__U21 => 0 null_a__and => 0 null_a__isNat => 0 null_a__plus => 0 null_mark => 0 null_A__U11 => 0 null_A__U21 => 0 null_A__AND => 0 null_A__ISNAT => 0 null_A__PLUS => 0 null_MARK => 0 ---------------------------------------- (50) 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__ISNAT(z0) :|: z = 1 + z0, z0 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__AND(a__isNat(z0), 1 + z1) + A__ISNAT(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__U11(a__isNat(z0), z0) + A__ISNAT(z0) :|: z = z0, z0 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__U21(a__and(a__isNat(z1), 1 + z0), z1, z0) + A__AND(a__isNat(z1), 1 + z0) + A__ISNAT(z1) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 A__U11(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__U11(z, z') -{ 1 }-> 1 + MARK(z0) :|: z = 1, z0 >= 0, z' = z0 A__U21(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 A__U21(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z1), mark(z0)) + MARK(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U21(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__ISNAT(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__U21(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U11(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 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') -{ 0 }-> mark(z0) :|: z = 1, z0 >= 0, z' = z0 a__U11(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U11(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U21(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U21(z, z', z'') -{ 0 }-> 1 + a__plus(mark(z1), mark(z0)) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U21(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__isNat(z0) :|: z = 1 + z0, z0 >= 0 a__isNat(z) -{ 0 }-> a__and(a__isNat(z0), 1 + 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__plus(z, z') -{ 0 }-> a__U21(a__and(a__isNat(z1), 1 + z0), z1, z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 a__plus(z, z') -{ 0 }-> a__U11(a__isNat(z0), z0) :|: z = z0, z0 >= 0, z' = 0 a__plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__plus(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 mark(z) -{ 0 }-> a__plus(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__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__U21(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U11(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 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. ---------------------------------------- (51) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U21(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) by A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, tt, x1) -> c2(A__PLUS(mark(x1), tt), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)), MARK(tt)) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)), MARK(0)) ---------------------------------------- (52) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c8(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) A__PLUS(z0, 0) -> c11(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, tt, x1) -> c2(A__PLUS(mark(x1), tt), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)), MARK(tt)) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)), MARK(0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c8(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) A__PLUS(z0, 0) -> c11(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, tt, x1) -> c2(A__PLUS(mark(x1), tt), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)), MARK(tt)) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_3, A__AND_2, A__ISNAT_1, A__PLUS_2, MARK_1 Compound Symbols: c_1, c3_2, c5_1, c8_2, c9_1, c11_2, c12_3, c14_2, c15_2, c16_2, c17_2, c18_2, c19_1, c21_1, c2_2 ---------------------------------------- (53) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (54) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c8(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) A__PLUS(z0, 0) -> c11(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c8(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) A__PLUS(z0, 0) -> c11(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__U21_3, A__AND_2, A__ISNAT_1, A__PLUS_2, MARK_1 Compound Symbols: c_1, c3_2, c5_1, c8_2, c9_1, c11_2, c12_3, c14_2, c15_2, c16_2, c17_2, c18_2, c19_1, c21_1, c2_2, c2_1 ---------------------------------------- (55) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U21(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) by A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, tt, x1) -> c3(A__PLUS(mark(x1), tt), MARK(tt)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0), MARK(0)) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c8(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) A__PLUS(z0, 0) -> c11(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, tt, x1) -> c3(A__PLUS(mark(x1), tt), MARK(tt)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0), MARK(0)) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c8(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) A__PLUS(z0, 0) -> c11(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, tt, x1) -> c3(A__PLUS(mark(x1), tt), MARK(tt)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0), MARK(0)) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, A__PLUS_2, MARK_1, A__U21_3 Compound Symbols: c_1, c5_1, c8_2, c9_1, c11_2, c12_3, c14_2, c15_2, c16_2, c17_2, c18_2, c19_1, c21_1, c2_2, c2_1, c3_2 ---------------------------------------- (57) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U21(tt, tt, x1) -> c3(A__PLUS(mark(x1), tt), MARK(tt)) ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c8(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) A__PLUS(z0, 0) -> c11(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0), MARK(0)) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c8(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) A__PLUS(z0, 0) -> c11(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0), MARK(0)) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, A__PLUS_2, MARK_1, A__U21_3 Compound Symbols: c_1, c5_1, c8_2, c9_1, c11_2, c12_3, c14_2, c15_2, c16_2, c17_2, c18_2, c19_1, c21_1, c2_2, c2_1, c3_2 ---------------------------------------- (59) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c8(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) A__PLUS(z0, 0) -> c11(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c8(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) A__PLUS(z0, 0) -> c11(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, A__PLUS_2, MARK_1, A__U21_3 Compound Symbols: c_1, c5_1, c8_2, c9_1, c11_2, c12_3, c14_2, c15_2, c16_2, c17_2, c18_2, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1 ---------------------------------------- (61) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ISNAT(plus(z0, z1)) -> c8(A__AND(a__isNat(z0), isNat(z1)), A__ISNAT(z0)) by A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1)), A__ISNAT(0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(z0, x1)) -> c8(A__AND(isNat(z0), isNat(x1)), A__ISNAT(z0)) ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) A__PLUS(z0, 0) -> c11(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1)), A__ISNAT(0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(z0, x1)) -> c8(A__AND(isNat(z0), isNat(x1)), A__ISNAT(z0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) A__PLUS(z0, 0) -> c11(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1)), A__ISNAT(0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(z0, x1)) -> c8(A__AND(isNat(z0), isNat(x1)), A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, A__PLUS_2, MARK_1, A__U21_3 Compound Symbols: c_1, c5_1, c9_1, c11_2, c12_3, c14_2, c15_2, c16_2, c17_2, c18_2, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2 ---------------------------------------- (63) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) A__PLUS(z0, 0) -> c11(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) A__PLUS(z0, 0) -> c11(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, A__PLUS_2, MARK_1, A__U21_3 Compound Symbols: c_1, c5_1, c9_1, c11_2, c12_3, c14_2, c15_2, c16_2, c17_2, c18_2, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1 ---------------------------------------- (65) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(z0, 0) -> c11(A__U11(a__isNat(z0), z0), A__ISNAT(z0)) by A__PLUS(0, 0) -> c11(A__U11(tt, 0), A__ISNAT(0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c11(A__U11(isNat(z0), z0), A__ISNAT(z0)) ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(0, 0) -> c11(A__U11(tt, 0), A__ISNAT(0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c11(A__U11(isNat(z0), z0), A__ISNAT(z0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(0, 0) -> c11(A__U11(tt, 0), A__ISNAT(0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(z0, 0) -> c11(A__U11(isNat(z0), z0), A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, A__PLUS_2, MARK_1, A__U21_3 Compound Symbols: c_1, c5_1, c9_1, c12_3, c14_2, c15_2, c16_2, c17_2, c18_2, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2 ---------------------------------------- (67) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, A__PLUS_2, MARK_1, A__U21_3 Compound Symbols: c_1, c5_1, c9_1, c12_3, c14_2, c15_2, c16_2, c17_2, c18_2, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1 ---------------------------------------- (69) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(z0, s(z1)) -> c12(A__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0), A__AND(a__isNat(z1), isNat(z0)), A__ISNAT(z1)) by A__PLUS(x0, s(x1)) -> c12(A__U21(and(a__isNat(x1), isNat(x0)), x1, x0), A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)), A__ISNAT(0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__U21(and(a__isNat(x1), isNat(x0)), x1, x0), A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)), A__ISNAT(0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__U21(and(a__isNat(x1), isNat(x0)), x1, x0), A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0)), A__ISNAT(0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c14_2, c15_2, c16_2, c17_2, c18_2, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3 ---------------------------------------- (71) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c14_2, c15_2, c16_2, c17_2, c18_2, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2 ---------------------------------------- (73) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U11(z0, z1)) -> c14(A__U11(mark(z0), z1), MARK(z0)) by MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1), MARK(tt)) MARK(U11(s(z0), x1)) -> c14(A__U11(s(mark(z0)), x1), MARK(s(z0))) MARK(U11(0, x1)) -> c14(A__U11(0, x1), MARK(0)) ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1), MARK(tt)) MARK(U11(s(z0), x1)) -> c14(A__U11(s(mark(z0)), x1), MARK(s(z0))) MARK(U11(0, x1)) -> c14(A__U11(0, x1), MARK(0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1), MARK(tt)) MARK(U11(s(z0), x1)) -> c14(A__U11(s(mark(z0)), x1), MARK(s(z0))) MARK(U11(0, x1)) -> c14(A__U11(0, x1), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c15_2, c16_2, c17_2, c18_2, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2 ---------------------------------------- (75) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U11(0, x1)) -> c14(A__U11(0, x1), MARK(0)) ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1), MARK(tt)) MARK(U11(s(z0), x1)) -> c14(A__U11(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1), MARK(tt)) MARK(U11(s(z0), x1)) -> c14(A__U11(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c15_2, c16_2, c17_2, c18_2, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2 ---------------------------------------- (77) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c15_2, c16_2, c17_2, c18_2, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1 ---------------------------------------- (79) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U21(z0, z1, z2)) -> c15(A__U21(mark(z0), z1, z2), MARK(z0)) by MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2), MARK(tt)) MARK(U21(s(z0), x1, x2)) -> c15(A__U21(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U21(0, x1, x2)) -> c15(A__U21(0, x1, x2), MARK(0)) ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2), MARK(tt)) MARK(U21(s(z0), x1, x2)) -> c15(A__U21(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U21(0, x1, x2)) -> c15(A__U21(0, x1, x2), MARK(0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2), MARK(tt)) MARK(U21(s(z0), x1, x2)) -> c15(A__U21(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U21(0, x1, x2)) -> c15(A__U21(0, x1, x2), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c16_2, c17_2, c18_2, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2 ---------------------------------------- (81) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U21(0, x1, x2)) -> c15(A__U21(0, x1, x2), MARK(0)) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2), MARK(tt)) MARK(U21(s(z0), x1, x2)) -> c15(A__U21(s(mark(z0)), x1, x2), MARK(s(z0))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2), MARK(tt)) MARK(U21(s(z0), x1, x2)) -> c15(A__U21(s(mark(z0)), x1, x2), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c16_2, c17_2, c18_2, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2 ---------------------------------------- (83) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c16_2, c17_2, c18_2, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1 ---------------------------------------- (85) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(z0, z1)) -> c16(A__PLUS(mark(z0), mark(z1)), MARK(z0)) by MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, tt)) -> c16(A__PLUS(mark(x0), tt), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1)), MARK(tt)) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1)), MARK(0)) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, tt)) -> c16(A__PLUS(mark(x0), tt), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1)), MARK(tt)) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1)), MARK(0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, tt)) -> c16(A__PLUS(mark(x0), tt), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1)), MARK(tt)) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c17_2, c18_2, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2 ---------------------------------------- (87) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c17_2, c18_2, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1 ---------------------------------------- (89) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(z0, z1)) -> c17(A__PLUS(mark(z0), mark(z1)), MARK(z1)) by MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, tt)) -> c17(A__PLUS(mark(x0), tt), MARK(tt)) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, tt)) -> c17(A__PLUS(mark(x0), tt), MARK(tt)) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, tt)) -> c17(A__PLUS(mark(x0), tt), MARK(tt)) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c18_2, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2 ---------------------------------------- (91) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(x0, tt)) -> c17(A__PLUS(mark(x0), tt), MARK(tt)) ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c18_2, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2 ---------------------------------------- (93) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c18_2, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1 ---------------------------------------- (95) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(z0, z1)) -> c18(A__AND(mark(z0), z1), MARK(z0)) by MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c18(A__AND(s(mark(z0)), x1), MARK(s(z0))) MARK(and(0, x1)) -> c18(A__AND(0, x1), MARK(0)) ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c18(A__AND(s(mark(z0)), x1), MARK(s(z0))) MARK(and(0, x1)) -> c18(A__AND(0, x1), MARK(0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c18(A__AND(s(mark(z0)), x1), MARK(s(z0))) MARK(and(0, x1)) -> c18(A__AND(0, x1), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2 ---------------------------------------- (97) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(and(0, x1)) -> c18(A__AND(0, x1), MARK(0)) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c18(A__AND(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c18(A__AND(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2 ---------------------------------------- (99) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (101) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U21(tt, U11(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) by A__U21(tt, U11(x0, z1), x2) -> c2(A__PLUS(mark(x2), U11(mark(x0), z1)), MARK(x2)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(tt)) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1)), MARK(0)) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(A__PLUS(mark(x2), U11(mark(x0), z1)), MARK(x2)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(tt)) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1)), MARK(0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(A__PLUS(mark(x2), U11(mark(x0), z1)), MARK(x2)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(tt)) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (103) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (105) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U21(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) by A__U21(tt, U21(x0, z1, z2), x3) -> c2(A__PLUS(mark(x3), U21(mark(x0), z1, z2)), MARK(x3)) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(tt)) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(0)) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(A__PLUS(mark(x3), U21(mark(x0), z1, z2)), MARK(x3)) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(tt)) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(A__PLUS(mark(x3), U21(mark(x0), z1, z2)), MARK(x3)) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(tt)) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (107) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (109) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U21(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) by A__U21(tt, plus(x0, x1), x2) -> c2(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(x2)) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(tt)) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(0)) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, x1), x2) -> c2(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(x2)) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(tt)) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, x1), x2) -> c2(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(x2)) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(tt)) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (111) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (113) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U21(tt, and(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(x1)) by A__U21(tt, and(x0, z1), x2) -> c2(A__PLUS(mark(x2), and(mark(x0), z1)), MARK(x2)) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1)), MARK(tt)) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1)), MARK(0)) ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(x0, z1), x2) -> c2(A__PLUS(mark(x2), and(mark(x0), z1)), MARK(x2)) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1)), MARK(tt)) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1)), MARK(0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(x0, z1), x2) -> c2(A__PLUS(mark(x2), and(mark(x0), z1)), MARK(x2)) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1)), MARK(tt)) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (115) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (117) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) by A__U21(tt, isNat(0), x1) -> c2(A__PLUS(mark(x1), tt), MARK(x1)) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0)), MARK(tt)) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0)), MARK(0)) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(0), x1) -> c2(A__PLUS(mark(x1), tt), MARK(x1)) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0)), MARK(tt)) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0)), MARK(0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(0), x1) -> c2(A__PLUS(mark(x1), tt), MARK(x1)) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(A__PLUS(mark(x1), isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0)), MARK(tt)) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (119) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (121) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U21(tt, x0, U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) by A__U21(tt, U11(z0, z1), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), a__U11(mark(z0), z1)), MARK(U11(x1, x2))) A__U21(tt, U21(z0, z1, z2), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), a__U21(mark(z0), z1, z2)), MARK(U11(x1, x2))) A__U21(tt, plus(z0, z1), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), a__plus(mark(z0), mark(z1))), MARK(U11(x1, x2))) A__U21(tt, and(z0, z1), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), a__and(mark(z0), z1)), MARK(U11(x1, x2))) A__U21(tt, isNat(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), a__isNat(z0)), MARK(U11(x1, x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), tt), MARK(U11(x1, x2))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0)), MARK(U11(0, x2))) ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, tt, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), tt), MARK(U11(x1, x2))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0)), MARK(U11(0, x2))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, tt, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), tt), MARK(U11(x1, x2))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0)), MARK(U11(0, x2))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (123) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) 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isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (125) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U21(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) by A__U21(tt, U11(z0, z1), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), a__U11(mark(z0), z1)), MARK(U21(x1, x2, x3))) A__U21(tt, U21(z0, z1, z2), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), a__U21(mark(z0), z1, z2)), MARK(U21(x1, x2, x3))) A__U21(tt, plus(z0, z1), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), a__plus(mark(z0), mark(z1))), MARK(U21(x1, x2, x3))) A__U21(tt, and(z0, z1), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), a__and(mark(z0), z1)), MARK(U21(x1, x2, x3))) A__U21(tt, isNat(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), a__isNat(z0)), MARK(U21(x1, x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), tt), MARK(U21(x1, x2, x3))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(U21(0, x2, x3))) ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), tt), MARK(U21(x1, x2, x3))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(U21(0, x2, x3))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), tt), MARK(U21(x1, x2, x3))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(U21(0, x2, x3))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (127) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (129) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U21(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) by A__U21(tt, U11(z0, z1), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), a__U11(mark(z0), z1)), MARK(plus(x1, x2))) A__U21(tt, U21(z0, z1, z2), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), a__U21(mark(z0), z1, z2)), MARK(plus(x1, x2))) A__U21(tt, plus(z0, z1), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), a__plus(mark(z0), mark(z1))), MARK(plus(x1, x2))) A__U21(tt, and(z0, z1), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), a__and(mark(z0), z1)), MARK(plus(x1, x2))) A__U21(tt, isNat(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), a__isNat(z0)), MARK(plus(x1, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(plus(x1, x2))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, tt, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(plus(x1, x2))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, tt, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(plus(x1, x2))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (131) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> 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a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (133) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U21(tt, x0, and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(and(z0, z1))) by A__U21(tt, U11(z0, z1), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), a__U11(mark(z0), z1)), MARK(and(x1, x2))) A__U21(tt, U21(z0, z1, z2), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), a__U21(mark(z0), z1, z2)), MARK(and(x1, x2))) A__U21(tt, plus(z0, z1), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), a__plus(mark(z0), mark(z1))), MARK(and(x1, x2))) A__U21(tt, and(z0, z1), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), a__and(mark(z0), z1)), MARK(and(x1, x2))) A__U21(tt, isNat(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), a__isNat(z0)), MARK(and(x1, x2))) A__U21(tt, tt, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), tt), MARK(and(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0)), MARK(and(0, x2))) ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> 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a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, tt, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), tt), MARK(and(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0)), MARK(and(0, x2))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), 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mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, tt, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), tt), MARK(and(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0)), MARK(and(0, x2))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (135) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, 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c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (137) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) by A__U21(tt, U11(z0, z1), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), a__U11(mark(z0), z1)), MARK(isNat(x1))) A__U21(tt, U21(z0, z1, z2), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), a__U21(mark(z0), z1, z2)), MARK(isNat(x1))) A__U21(tt, plus(z0, z1), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), a__plus(mark(z0), mark(z1))), MARK(isNat(x1))) A__U21(tt, and(z0, z1), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), a__and(mark(z0), z1)), MARK(isNat(x1))) A__U21(tt, isNat(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), a__isNat(z0)), MARK(isNat(x1))) A__U21(tt, tt, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), tt), MARK(isNat(x1))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, tt, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), tt), MARK(isNat(x1))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, tt, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), tt), MARK(isNat(x1))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (139) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (141) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U21(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) by A__U21(tt, U11(z0, z1), s(x1)) -> c2(A__PLUS(s(mark(x1)), a__U11(mark(z0), z1)), MARK(s(x1))) A__U21(tt, U21(z0, z1, z2), s(x1)) -> c2(A__PLUS(s(mark(x1)), a__U21(mark(z0), z1, z2)), MARK(s(x1))) A__U21(tt, plus(z0, z1), s(x1)) -> c2(A__PLUS(s(mark(x1)), a__plus(mark(z0), mark(z1))), MARK(s(x1))) A__U21(tt, and(z0, z1), s(x1)) -> c2(A__PLUS(s(mark(x1)), a__and(mark(z0), z1)), MARK(s(x1))) A__U21(tt, isNat(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), a__isNat(z0)), MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(A__PLUS(s(mark(x1)), tt), MARK(s(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, tt, s(x1)) -> c2(A__PLUS(s(mark(x1)), tt), MARK(s(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, tt, s(x1)) -> c2(A__PLUS(s(mark(x1)), tt), MARK(s(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (143) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (145) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U21(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) by A__U21(tt, U11(z0, z1), tt) -> c2(A__PLUS(tt, a__U11(mark(z0), z1))) A__U21(tt, U21(z0, z1, z2), tt) -> c2(A__PLUS(tt, a__U21(mark(z0), z1, z2))) A__U21(tt, plus(z0, z1), tt) -> c2(A__PLUS(tt, a__plus(mark(z0), mark(z1)))) A__U21(tt, and(z0, z1), tt) -> c2(A__PLUS(tt, a__and(mark(z0), z1))) A__U21(tt, isNat(z0), tt) -> c2(A__PLUS(tt, a__isNat(z0))) A__U21(tt, tt, tt) -> c2(A__PLUS(tt, tt)) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, tt) -> c2(A__PLUS(tt, tt)) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, tt) -> c2(A__PLUS(tt, tt)) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (147) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U21(tt, tt, tt) -> c2(A__PLUS(tt, tt)) ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (149) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U21(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) by A__U21(tt, U11(z0, z1), 0) -> c2(A__PLUS(0, a__U11(mark(z0), z1))) A__U21(tt, U21(z0, z1, z2), 0) -> c2(A__PLUS(0, a__U21(mark(z0), z1, z2))) A__U21(tt, plus(z0, z1), 0) -> c2(A__PLUS(0, a__plus(mark(z0), mark(z1)))) A__U21(tt, and(z0, z1), 0) -> c2(A__PLUS(0, a__and(mark(z0), z1))) A__U21(tt, isNat(z0), 0) -> c2(A__PLUS(0, a__isNat(z0))) A__U21(tt, tt, 0) -> c2(A__PLUS(0, tt)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, tt, 0) -> c2(A__PLUS(0, tt)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, tt, 0) -> c2(A__PLUS(0, tt)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (151) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U21(tt, tt, 0) -> c2(A__PLUS(0, tt)) ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), 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x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (153) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U21(tt, U11(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) by A__U21(tt, U11(x0, z1), x2) -> c3(A__PLUS(mark(x2), U11(mark(x0), z1)), MARK(U11(x0, z1))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1)), MARK(U11(0, x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(x0, z1), x2) -> c3(A__PLUS(mark(x2), U11(mark(x0), z1)), MARK(U11(x0, z1))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1)), MARK(U11(0, x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), 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c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(x0, z1), x2) -> c3(A__PLUS(mark(x2), U11(mark(x0), z1)), MARK(U11(x0, z1))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1)), MARK(U11(0, x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (155) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), 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x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (157) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U21(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) by A__U21(tt, U21(x0, z1, z2), x3) -> c3(A__PLUS(mark(x3), U21(mark(x0), z1, z2)), MARK(U21(x0, z1, z2))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(U21(0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, 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x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(A__PLUS(mark(x3), U21(mark(x0), z1, z2)), MARK(U21(x0, z1, z2))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(U21(0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), 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c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(A__PLUS(mark(x3), U21(mark(x0), z1, z2)), MARK(U21(x0, z1, z2))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(U21(0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (159) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, 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U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), 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x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (161) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U21(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) by A__U21(tt, plus(x0, x1), x2) -> c3(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) ---------------------------------------- (162) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> 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A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, x1), x2) -> c3(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> 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MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, x1), x2) -> c3(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (163) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), 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z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) 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x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (165) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U21(tt, and(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) by A__U21(tt, and(x0, z1), x2) -> c3(A__PLUS(mark(x2), and(mark(x0), z1)), MARK(and(x0, z1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1)), MARK(and(0, x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) ---------------------------------------- (166) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, 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A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(A__PLUS(mark(x2), and(mark(x0), z1)), MARK(and(x0, z1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1)), MARK(and(0, x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(A__PLUS(mark(x2), and(mark(x0), z1)), MARK(and(x0, z1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1)), MARK(and(0, x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (167) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (168) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, 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mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (169) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) by A__U21(tt, isNat(0), x1) -> c3(A__PLUS(mark(x1), tt), MARK(isNat(0))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), isNat(z0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) ---------------------------------------- (170) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, 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c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(0), x1) -> c3(A__PLUS(mark(x1), tt), MARK(isNat(0))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), isNat(z0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(0), x1) -> c3(A__PLUS(mark(x1), tt), MARK(isNat(0))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(z0), x1) -> c3(A__PLUS(mark(x1), isNat(z0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (171) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (172) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, 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x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, 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c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (173) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U21(tt, x0, U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) by A__U21(tt, U11(z0, z1), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, tt, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), tt), MARK(tt)) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0), MARK(0)) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) ---------------------------------------- (174) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, tt, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), tt), MARK(tt)) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0), MARK(0)) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), 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x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, tt, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), tt), MARK(tt)) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0), MARK(0)) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (175) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U21(tt, tt, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), tt), MARK(tt)) ---------------------------------------- (176) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), 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U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0), MARK(0)) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), 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A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0), MARK(0)) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (177) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (178) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, 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A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), 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c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (179) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U21(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) by A__U21(tt, U11(z0, z1), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, tt, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), tt), MARK(tt)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(0)) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) ---------------------------------------- (180) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), 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c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, tt, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), tt), MARK(tt)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(0)) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, tt, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), tt), MARK(tt)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(0)) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (181) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U21(tt, tt, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), tt), MARK(tt)) ---------------------------------------- (182) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(0)) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 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mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(0)) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (183) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (184) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, 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c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> 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z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (185) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U21(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) by A__U21(tt, U11(z0, z1), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, tt, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(tt)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(0)) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) ---------------------------------------- (186) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, 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MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, tt, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(tt)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(0)) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, 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c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, 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x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, tt, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(tt)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(0)) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (187) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U21(tt, tt, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(tt)) ---------------------------------------- (188) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(0)) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(0)) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (189) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (190) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) 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c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> 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c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (191) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U21(tt, x0, and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x0)), MARK(x0)) by A__U21(tt, U11(z0, z1), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, tt, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), tt), MARK(tt)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0), MARK(0)) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) ---------------------------------------- (192) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), 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MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), 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a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, 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x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, tt, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), tt), MARK(tt)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0), MARK(0)) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) 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U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, tt, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), tt), MARK(tt)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0), MARK(0)) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (193) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U21(tt, tt, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), tt), MARK(tt)) ---------------------------------------- (194) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), 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U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0), MARK(0)) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0), MARK(0)) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (195) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (196) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, 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A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), 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U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, 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mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (197) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) by A__U21(tt, U11(z0, z1), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), tt), MARK(tt)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0), MARK(0)) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) ---------------------------------------- (198) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, tt, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), tt), MARK(tt)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0), MARK(0)) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, tt, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), tt), MARK(tt)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0), MARK(0)) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (199) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U21(tt, tt, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), tt), MARK(tt)) ---------------------------------------- (200) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> 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c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0), MARK(0)) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> 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a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0), MARK(0)) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (201) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (202) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, 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A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> 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0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, 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x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> 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a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), 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x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (203) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U21(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) by A__U21(tt, U11(z0, z1), tt) -> c3(A__PLUS(tt, a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), tt) -> c3(A__PLUS(tt, a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), tt) -> c3(A__PLUS(tt, a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), tt) -> c3(A__PLUS(tt, a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), tt) -> c3(A__PLUS(tt, a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, tt, tt) -> c3(A__PLUS(tt, tt), MARK(tt)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0), MARK(0)) ---------------------------------------- (204) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, tt, tt) -> c3(A__PLUS(tt, tt), MARK(tt)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0), MARK(0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), 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x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), 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A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, tt, tt) -> c3(A__PLUS(tt, tt), MARK(tt)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (205) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U21(tt, tt, tt) -> c3(A__PLUS(tt, tt), MARK(tt)) ---------------------------------------- (206) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), 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x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> 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z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), 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c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0), MARK(0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), 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c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (207) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (208) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, 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a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), 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x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), 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A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (209) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U21(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) by A__U21(tt, U11(z0, z1), s(x1)) -> c3(A__PLUS(s(mark(x1)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), s(x1)) -> c3(A__PLUS(s(mark(x1)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), s(x1)) -> c3(A__PLUS(s(mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), s(x1)) -> c3(A__PLUS(s(mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, tt, s(x1)) -> c3(A__PLUS(s(mark(x1)), tt), MARK(tt)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0), MARK(0)) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) ---------------------------------------- (210) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, 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MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, tt, s(x1)) -> c3(A__PLUS(s(mark(x1)), tt), MARK(tt)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0), MARK(0)) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, tt, s(x1)) -> c3(A__PLUS(s(mark(x1)), tt), MARK(tt)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0), MARK(0)) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (211) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U21(tt, tt, s(x1)) -> c3(A__PLUS(s(mark(x1)), tt), MARK(tt)) ---------------------------------------- (212) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0), MARK(0)) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, 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tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0), MARK(0)) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (213) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (214) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> 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a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> 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a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (215) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U21(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0)) by A__U21(tt, U11(z0, z1), 0) -> c3(A__PLUS(0, a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U21(tt, U21(z0, z1, z2), 0) -> c3(A__PLUS(0, a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) A__U21(tt, plus(z0, z1), 0) -> c3(A__PLUS(0, a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U21(tt, and(z0, z1), 0) -> c3(A__PLUS(0, a__and(mark(z0), z1)), MARK(and(z0, z1))) A__U21(tt, isNat(z0), 0) -> c3(A__PLUS(0, a__isNat(z0)), MARK(isNat(z0))) A__U21(tt, tt, 0) -> c3(A__PLUS(0, tt), MARK(tt)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0), MARK(0)) ---------------------------------------- (216) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) 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MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, tt, 0) -> c3(A__PLUS(0, tt), MARK(tt)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0), MARK(0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, 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mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, tt, 0) -> c3(A__PLUS(0, tt), MARK(tt)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (217) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U21(tt, tt, 0) -> c3(A__PLUS(0, tt), MARK(tt)) ---------------------------------------- (218) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), 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U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0), MARK(0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), 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a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> 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plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, 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z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (219) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (220) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> 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c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), 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c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), 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x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (221) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ISNAT(plus(plus(z0, z1), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(plus(z0, z1))) by A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__AND(and(a__isNat(x0), isNat(x1)), isNat(x2)), A__ISNAT(plus(x0, x1))) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) ---------------------------------------- (222) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), 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mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__AND(and(a__isNat(x0), isNat(x1)), isNat(x2)), A__ISNAT(plus(x0, x1))) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__AND(and(a__isNat(x0), isNat(x1)), isNat(x2)), A__ISNAT(plus(x0, x1))) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (223) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (224) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, 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MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__ISNAT(plus(x0, x1))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), 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c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__ISNAT(plus(x0, x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_2, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1 ---------------------------------------- (225) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(z0))) by A__ISNAT(plus(s(0), x1)) -> c8(A__AND(tt, isNat(x1)), A__ISNAT(s(0))) A__ISNAT(plus(s(plus(z0, z1)), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(s(plus(z0, z1)))) A__ISNAT(plus(s(s(z0)), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(s(z0)))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(isNat(z0), isNat(x1)), A__ISNAT(s(z0))) ---------------------------------------- (226) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> 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A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), 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z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), 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plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__ISNAT(plus(x0, x1))) A__ISNAT(plus(s(0), x1)) -> c8(A__AND(tt, isNat(x1)), A__ISNAT(s(0))) A__ISNAT(plus(s(plus(z0, z1)), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(s(plus(z0, z1)))) A__ISNAT(plus(s(s(z0)), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(s(z0)))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(isNat(z0), isNat(x1)), A__ISNAT(s(z0))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), 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A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__ISNAT(plus(x0, x1))) A__ISNAT(plus(s(0), x1)) -> c8(A__AND(tt, isNat(x1)), A__ISNAT(s(0))) A__ISNAT(plus(s(plus(z0, z1)), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(s(plus(z0, z1)))) A__ISNAT(plus(s(s(z0)), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(s(z0)))) A__ISNAT(plus(s(z0), x1)) -> c8(A__AND(isNat(z0), isNat(x1)), A__ISNAT(s(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1, c8_2 ---------------------------------------- (227) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (228) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, 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MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__ISNAT(plus(x0, x1))) A__ISNAT(plus(s(0), x1)) -> c8(A__AND(tt, isNat(x1)), A__ISNAT(s(0))) A__ISNAT(plus(s(plus(z0, z1)), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(s(plus(z0, z1)))) A__ISNAT(plus(s(s(z0)), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(s(z0)))) A__ISNAT(plus(s(z0), x1)) -> c8(A__ISNAT(s(z0))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), 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U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__ISNAT(plus(x0, x1))) A__ISNAT(plus(s(0), x1)) -> c8(A__AND(tt, isNat(x1)), A__ISNAT(s(0))) A__ISNAT(plus(s(plus(z0, z1)), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(s(plus(z0, z1)))) A__ISNAT(plus(s(s(z0)), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(s(z0)))) A__ISNAT(plus(s(z0), x1)) -> c8(A__ISNAT(s(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1, c8_2 ---------------------------------------- (229) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(plus(z0, z1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), plus(z0, z1)), A__ISNAT(plus(z0, z1))) by A__PLUS(plus(x0, x1), 0) -> c11(A__U11(and(a__isNat(x0), isNat(x1)), plus(x0, x1)), A__ISNAT(plus(x0, x1))) A__PLUS(plus(0, x1), 0) -> c11(A__U11(a__and(tt, isNat(x1)), plus(0, x1)), A__ISNAT(plus(0, x1))) A__PLUS(plus(plus(z0, z1), x1), 0) -> c11(A__U11(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), plus(plus(z0, z1), x1)), A__ISNAT(plus(plus(z0, z1), x1))) A__PLUS(plus(s(z0), x1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(x1)), plus(s(z0), x1)), A__ISNAT(plus(s(z0), x1))) A__PLUS(plus(z0, x1), 0) -> c11(A__U11(a__and(isNat(z0), isNat(x1)), plus(z0, x1)), A__ISNAT(plus(z0, x1))) ---------------------------------------- (230) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, 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A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__ISNAT(plus(x0, x1))) A__ISNAT(plus(s(0), x1)) -> c8(A__AND(tt, isNat(x1)), A__ISNAT(s(0))) A__ISNAT(plus(s(plus(z0, z1)), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(s(plus(z0, z1)))) A__ISNAT(plus(s(s(z0)), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(s(z0)))) A__ISNAT(plus(s(z0), x1)) -> c8(A__ISNAT(s(z0))) A__PLUS(plus(x0, x1), 0) -> c11(A__U11(and(a__isNat(x0), isNat(x1)), plus(x0, x1)), A__ISNAT(plus(x0, x1))) A__PLUS(plus(0, x1), 0) -> c11(A__U11(a__and(tt, isNat(x1)), plus(0, x1)), A__ISNAT(plus(0, x1))) A__PLUS(plus(plus(z0, z1), x1), 0) -> c11(A__U11(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), plus(plus(z0, z1), x1)), A__ISNAT(plus(plus(z0, z1), x1))) A__PLUS(plus(s(z0), x1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(x1)), plus(s(z0), x1)), A__ISNAT(plus(s(z0), x1))) A__PLUS(plus(z0, x1), 0) -> c11(A__U11(a__and(isNat(z0), isNat(x1)), plus(z0, x1)), A__ISNAT(plus(z0, x1))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__ISNAT(plus(x0, x1))) A__ISNAT(plus(s(0), x1)) -> c8(A__AND(tt, isNat(x1)), A__ISNAT(s(0))) A__ISNAT(plus(s(plus(z0, z1)), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(s(plus(z0, z1)))) A__ISNAT(plus(s(s(z0)), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(s(z0)))) A__ISNAT(plus(s(z0), x1)) -> c8(A__ISNAT(s(z0))) A__PLUS(plus(x0, x1), 0) -> c11(A__U11(and(a__isNat(x0), isNat(x1)), plus(x0, x1)), A__ISNAT(plus(x0, x1))) A__PLUS(plus(0, x1), 0) -> c11(A__U11(a__and(tt, isNat(x1)), plus(0, x1)), A__ISNAT(plus(0, x1))) A__PLUS(plus(plus(z0, z1), x1), 0) -> c11(A__U11(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), plus(plus(z0, z1), x1)), A__ISNAT(plus(plus(z0, z1), x1))) A__PLUS(plus(s(z0), x1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(x1)), plus(s(z0), x1)), A__ISNAT(plus(s(z0), x1))) A__PLUS(plus(z0, x1), 0) -> c11(A__U11(a__and(isNat(z0), isNat(x1)), plus(z0, x1)), A__ISNAT(plus(z0, x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1, c8_2 ---------------------------------------- (231) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (232) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) 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c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__ISNAT(plus(x0, x1))) A__ISNAT(plus(s(0), x1)) -> c8(A__AND(tt, isNat(x1)), A__ISNAT(s(0))) A__ISNAT(plus(s(plus(z0, z1)), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(s(plus(z0, z1)))) A__ISNAT(plus(s(s(z0)), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(s(z0)))) A__ISNAT(plus(s(z0), x1)) -> c8(A__ISNAT(s(z0))) A__PLUS(plus(0, x1), 0) -> c11(A__U11(a__and(tt, isNat(x1)), plus(0, x1)), A__ISNAT(plus(0, x1))) A__PLUS(plus(plus(z0, z1), x1), 0) -> c11(A__U11(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), plus(plus(z0, z1), x1)), A__ISNAT(plus(plus(z0, z1), x1))) A__PLUS(plus(s(z0), x1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(x1)), plus(s(z0), x1)), A__ISNAT(plus(s(z0), x1))) A__PLUS(plus(z0, x1), 0) -> c11(A__U11(a__and(isNat(z0), isNat(x1)), plus(z0, x1)), A__ISNAT(plus(z0, x1))) A__PLUS(plus(x0, x1), 0) -> c11(A__ISNAT(plus(x0, x1))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), 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plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__ISNAT(plus(x0, x1))) A__ISNAT(plus(s(0), x1)) -> c8(A__AND(tt, isNat(x1)), A__ISNAT(s(0))) A__ISNAT(plus(s(plus(z0, z1)), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(s(plus(z0, z1)))) A__ISNAT(plus(s(s(z0)), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(s(z0)))) A__ISNAT(plus(s(z0), x1)) -> c8(A__ISNAT(s(z0))) A__PLUS(plus(0, x1), 0) -> c11(A__U11(a__and(tt, isNat(x1)), plus(0, x1)), A__ISNAT(plus(0, x1))) A__PLUS(plus(plus(z0, z1), x1), 0) -> c11(A__U11(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), plus(plus(z0, z1), x1)), A__ISNAT(plus(plus(z0, z1), x1))) A__PLUS(plus(s(z0), x1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(x1)), plus(s(z0), x1)), A__ISNAT(plus(s(z0), x1))) A__PLUS(plus(z0, x1), 0) -> c11(A__U11(a__and(isNat(z0), isNat(x1)), plus(z0, x1)), A__ISNAT(plus(z0, x1))) A__PLUS(plus(x0, x1), 0) -> c11(A__ISNAT(plus(x0, x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_1, c11_2, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1, c8_2 ---------------------------------------- (233) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(s(z0), 0) -> c11(A__U11(a__isNat(z0), s(z0)), A__ISNAT(s(z0))) by A__PLUS(s(0), 0) -> c11(A__U11(tt, s(0)), A__ISNAT(s(0))) A__PLUS(s(plus(z0, z1)), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__PLUS(s(s(z0)), 0) -> c11(A__U11(a__isNat(z0), s(s(z0))), A__ISNAT(s(s(z0)))) A__PLUS(s(z0), 0) -> c11(A__U11(isNat(z0), s(z0)), A__ISNAT(s(z0))) ---------------------------------------- (234) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, 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MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__ISNAT(plus(x0, x1))) A__ISNAT(plus(s(0), x1)) -> c8(A__AND(tt, isNat(x1)), A__ISNAT(s(0))) A__ISNAT(plus(s(plus(z0, z1)), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(s(plus(z0, z1)))) A__ISNAT(plus(s(s(z0)), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(s(z0)))) A__ISNAT(plus(s(z0), x1)) -> c8(A__ISNAT(s(z0))) A__PLUS(plus(0, x1), 0) -> c11(A__U11(a__and(tt, isNat(x1)), plus(0, x1)), A__ISNAT(plus(0, x1))) A__PLUS(plus(plus(z0, z1), x1), 0) -> c11(A__U11(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), plus(plus(z0, z1), x1)), A__ISNAT(plus(plus(z0, z1), x1))) A__PLUS(plus(s(z0), x1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(x1)), plus(s(z0), x1)), A__ISNAT(plus(s(z0), x1))) A__PLUS(plus(z0, x1), 0) -> c11(A__U11(a__and(isNat(z0), isNat(x1)), plus(z0, x1)), A__ISNAT(plus(z0, x1))) A__PLUS(plus(x0, x1), 0) -> c11(A__ISNAT(plus(x0, x1))) A__PLUS(s(0), 0) -> c11(A__U11(tt, s(0)), A__ISNAT(s(0))) A__PLUS(s(plus(z0, z1)), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__PLUS(s(s(z0)), 0) -> c11(A__U11(a__isNat(z0), s(s(z0))), A__ISNAT(s(s(z0)))) A__PLUS(s(z0), 0) -> c11(A__U11(isNat(z0), s(z0)), A__ISNAT(s(z0))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), 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U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__ISNAT(plus(x0, x1))) A__ISNAT(plus(s(0), x1)) -> c8(A__AND(tt, isNat(x1)), A__ISNAT(s(0))) A__ISNAT(plus(s(plus(z0, z1)), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(s(plus(z0, z1)))) A__ISNAT(plus(s(s(z0)), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(s(z0)))) A__ISNAT(plus(s(z0), x1)) -> c8(A__ISNAT(s(z0))) A__PLUS(plus(0, x1), 0) -> c11(A__U11(a__and(tt, isNat(x1)), plus(0, x1)), A__ISNAT(plus(0, x1))) A__PLUS(plus(plus(z0, z1), x1), 0) -> c11(A__U11(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), plus(plus(z0, z1), x1)), A__ISNAT(plus(plus(z0, z1), x1))) A__PLUS(plus(s(z0), x1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(x1)), plus(s(z0), x1)), A__ISNAT(plus(s(z0), x1))) A__PLUS(plus(z0, x1), 0) -> c11(A__U11(a__and(isNat(z0), isNat(x1)), plus(z0, x1)), A__ISNAT(plus(z0, x1))) A__PLUS(plus(x0, x1), 0) -> c11(A__ISNAT(plus(x0, x1))) A__PLUS(s(0), 0) -> c11(A__U11(tt, s(0)), A__ISNAT(s(0))) A__PLUS(s(plus(z0, z1)), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__PLUS(s(s(z0)), 0) -> c11(A__U11(a__isNat(z0), s(s(z0))), A__ISNAT(s(s(z0)))) A__PLUS(s(z0), 0) -> c11(A__U11(isNat(z0), s(z0)), A__ISNAT(s(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_1, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1, c8_2, c11_2 ---------------------------------------- (235) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (236) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__ISNAT(plus(x0, x1))) A__ISNAT(plus(s(0), x1)) -> c8(A__AND(tt, isNat(x1)), A__ISNAT(s(0))) A__ISNAT(plus(s(plus(z0, z1)), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(s(plus(z0, z1)))) A__ISNAT(plus(s(s(z0)), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(s(z0)))) A__ISNAT(plus(s(z0), x1)) -> c8(A__ISNAT(s(z0))) A__PLUS(plus(0, x1), 0) -> c11(A__U11(a__and(tt, isNat(x1)), plus(0, x1)), A__ISNAT(plus(0, x1))) A__PLUS(plus(plus(z0, z1), x1), 0) -> c11(A__U11(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), plus(plus(z0, z1), x1)), A__ISNAT(plus(plus(z0, z1), x1))) A__PLUS(plus(s(z0), x1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(x1)), plus(s(z0), x1)), A__ISNAT(plus(s(z0), x1))) A__PLUS(plus(z0, x1), 0) -> c11(A__U11(a__and(isNat(z0), isNat(x1)), plus(z0, x1)), A__ISNAT(plus(z0, x1))) A__PLUS(plus(x0, x1), 0) -> c11(A__ISNAT(plus(x0, x1))) A__PLUS(s(0), 0) -> c11(A__U11(tt, s(0)), A__ISNAT(s(0))) A__PLUS(s(plus(z0, z1)), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__PLUS(s(s(z0)), 0) -> c11(A__U11(a__isNat(z0), s(s(z0))), A__ISNAT(s(s(z0)))) A__PLUS(s(z0), 0) -> c11(A__ISNAT(s(z0))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> 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x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), 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a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__ISNAT(plus(x0, x1))) A__ISNAT(plus(s(0), x1)) -> c8(A__AND(tt, isNat(x1)), A__ISNAT(s(0))) A__ISNAT(plus(s(plus(z0, z1)), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(s(plus(z0, z1)))) A__ISNAT(plus(s(s(z0)), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(s(z0)))) A__ISNAT(plus(s(z0), x1)) -> c8(A__ISNAT(s(z0))) A__PLUS(plus(0, x1), 0) -> c11(A__U11(a__and(tt, isNat(x1)), plus(0, x1)), A__ISNAT(plus(0, x1))) A__PLUS(plus(plus(z0, z1), x1), 0) -> c11(A__U11(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), plus(plus(z0, z1), x1)), A__ISNAT(plus(plus(z0, z1), x1))) A__PLUS(plus(s(z0), x1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(x1)), plus(s(z0), x1)), A__ISNAT(plus(s(z0), x1))) A__PLUS(plus(z0, x1), 0) -> c11(A__U11(a__and(isNat(z0), isNat(x1)), plus(z0, x1)), A__ISNAT(plus(z0, x1))) A__PLUS(plus(x0, x1), 0) -> c11(A__ISNAT(plus(x0, x1))) A__PLUS(s(0), 0) -> c11(A__U11(tt, s(0)), A__ISNAT(s(0))) A__PLUS(s(plus(z0, z1)), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__PLUS(s(s(z0)), 0) -> c11(A__U11(a__isNat(z0), s(s(z0))), A__ISNAT(s(s(z0)))) A__PLUS(s(z0), 0) -> c11(A__ISNAT(s(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_1, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1, c8_2, c11_2 ---------------------------------------- (237) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(x0, s(plus(z0, z1))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), plus(z0, z1), x0), A__AND(a__isNat(plus(z0, z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) by A__PLUS(x0, s(plus(x1, x2))) -> c12(A__U21(and(a__and(a__isNat(x1), isNat(x2)), isNat(x0)), plus(x1, x2), x0), A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__U21(a__and(and(a__isNat(x1), isNat(x2)), isNat(x0)), plus(x1, x2), x0), A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(plus(0, x2))) -> c12(A__U21(a__and(a__and(tt, isNat(x2)), isNat(x0)), plus(0, x2), x0), A__AND(a__isNat(plus(0, x2)), isNat(x0)), A__ISNAT(plus(0, x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c12(A__U21(a__and(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x2)), isNat(x0)), plus(plus(z0, z1), x2), x0), A__AND(a__isNat(plus(plus(z0, z1), x2)), isNat(x0)), A__ISNAT(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(x2)), isNat(x0)), plus(s(z0), x2), x0), A__AND(a__isNat(plus(s(z0), x2)), isNat(x0)), A__ISNAT(plus(s(z0), x2))) A__PLUS(x0, s(plus(z0, x2))) -> c12(A__U21(a__and(a__and(isNat(z0), isNat(x2)), isNat(x0)), plus(z0, x2), x0), A__AND(a__isNat(plus(z0, x2)), isNat(x0)), A__ISNAT(plus(z0, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0))) ---------------------------------------- (238) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> 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A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), 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z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), 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plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__ISNAT(plus(x0, x1))) A__ISNAT(plus(s(0), x1)) -> c8(A__AND(tt, isNat(x1)), A__ISNAT(s(0))) A__ISNAT(plus(s(plus(z0, z1)), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(s(plus(z0, z1)))) A__ISNAT(plus(s(s(z0)), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(s(z0)))) A__ISNAT(plus(s(z0), x1)) -> c8(A__ISNAT(s(z0))) A__PLUS(plus(0, x1), 0) -> c11(A__U11(a__and(tt, isNat(x1)), plus(0, x1)), A__ISNAT(plus(0, x1))) A__PLUS(plus(plus(z0, z1), x1), 0) -> c11(A__U11(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), plus(plus(z0, z1), x1)), A__ISNAT(plus(plus(z0, z1), x1))) A__PLUS(plus(s(z0), x1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(x1)), plus(s(z0), x1)), A__ISNAT(plus(s(z0), x1))) A__PLUS(plus(z0, x1), 0) -> c11(A__U11(a__and(isNat(z0), isNat(x1)), plus(z0, x1)), A__ISNAT(plus(z0, x1))) A__PLUS(plus(x0, x1), 0) -> c11(A__ISNAT(plus(x0, x1))) A__PLUS(s(0), 0) -> c11(A__U11(tt, s(0)), A__ISNAT(s(0))) A__PLUS(s(plus(z0, z1)), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__PLUS(s(s(z0)), 0) -> c11(A__U11(a__isNat(z0), s(s(z0))), A__ISNAT(s(s(z0)))) A__PLUS(s(z0), 0) -> c11(A__ISNAT(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__U21(and(a__and(a__isNat(x1), isNat(x2)), isNat(x0)), plus(x1, x2), x0), A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__U21(a__and(and(a__isNat(x1), isNat(x2)), isNat(x0)), plus(x1, x2), x0), A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(plus(0, x2))) -> c12(A__U21(a__and(a__and(tt, isNat(x2)), isNat(x0)), plus(0, x2), x0), A__AND(a__isNat(plus(0, x2)), isNat(x0)), A__ISNAT(plus(0, x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c12(A__U21(a__and(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x2)), isNat(x0)), plus(plus(z0, z1), x2), x0), A__AND(a__isNat(plus(plus(z0, z1), x2)), isNat(x0)), A__ISNAT(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(x2)), isNat(x0)), plus(s(z0), x2), x0), A__AND(a__isNat(plus(s(z0), x2)), isNat(x0)), A__ISNAT(plus(s(z0), x2))) A__PLUS(x0, s(plus(z0, x2))) -> c12(A__U21(a__and(a__and(isNat(z0), isNat(x2)), isNat(x0)), plus(z0, x2), x0), A__AND(a__isNat(plus(z0, x2)), isNat(x0)), A__ISNAT(plus(z0, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__ISNAT(plus(x0, x1))) A__ISNAT(plus(s(0), x1)) -> c8(A__AND(tt, isNat(x1)), A__ISNAT(s(0))) A__ISNAT(plus(s(plus(z0, z1)), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(s(plus(z0, z1)))) A__ISNAT(plus(s(s(z0)), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(s(z0)))) A__ISNAT(plus(s(z0), x1)) -> c8(A__ISNAT(s(z0))) A__PLUS(plus(0, x1), 0) -> c11(A__U11(a__and(tt, isNat(x1)), plus(0, x1)), A__ISNAT(plus(0, x1))) A__PLUS(plus(plus(z0, z1), x1), 0) -> c11(A__U11(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), plus(plus(z0, z1), x1)), A__ISNAT(plus(plus(z0, z1), x1))) A__PLUS(plus(s(z0), x1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(x1)), plus(s(z0), x1)), A__ISNAT(plus(s(z0), x1))) A__PLUS(plus(z0, x1), 0) -> c11(A__U11(a__and(isNat(z0), isNat(x1)), plus(z0, x1)), A__ISNAT(plus(z0, x1))) A__PLUS(plus(x0, x1), 0) -> c11(A__ISNAT(plus(x0, x1))) A__PLUS(s(0), 0) -> c11(A__U11(tt, s(0)), A__ISNAT(s(0))) A__PLUS(s(plus(z0, z1)), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__PLUS(s(s(z0)), 0) -> c11(A__U11(a__isNat(z0), s(s(z0))), A__ISNAT(s(s(z0)))) A__PLUS(s(z0), 0) -> c11(A__ISNAT(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__U21(and(a__and(a__isNat(x1), isNat(x2)), isNat(x0)), plus(x1, x2), x0), A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__U21(a__and(and(a__isNat(x1), isNat(x2)), isNat(x0)), plus(x1, x2), x0), A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(plus(0, x2))) -> c12(A__U21(a__and(a__and(tt, isNat(x2)), isNat(x0)), plus(0, x2), x0), A__AND(a__isNat(plus(0, x2)), isNat(x0)), A__ISNAT(plus(0, x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c12(A__U21(a__and(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x2)), isNat(x0)), plus(plus(z0, z1), x2), x0), A__AND(a__isNat(plus(plus(z0, z1), x2)), isNat(x0)), A__ISNAT(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(x2)), isNat(x0)), plus(s(z0), x2), x0), A__AND(a__isNat(plus(s(z0), x2)), isNat(x0)), A__ISNAT(plus(s(z0), x2))) A__PLUS(x0, s(plus(z0, x2))) -> c12(A__U21(a__and(a__and(isNat(z0), isNat(x2)), isNat(x0)), plus(z0, x2), x0), A__AND(a__isNat(plus(z0, x2)), isNat(x0)), A__ISNAT(plus(z0, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_1, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1, c8_2, c11_2, c12_1 ---------------------------------------- (239) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (240) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> 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A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) 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A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), 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x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__ISNAT(plus(x0, x1))) A__ISNAT(plus(s(0), x1)) -> c8(A__AND(tt, isNat(x1)), A__ISNAT(s(0))) A__ISNAT(plus(s(plus(z0, z1)), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(s(plus(z0, z1)))) A__ISNAT(plus(s(s(z0)), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(s(z0)))) A__ISNAT(plus(s(z0), x1)) -> c8(A__ISNAT(s(z0))) A__PLUS(plus(0, x1), 0) -> c11(A__U11(a__and(tt, isNat(x1)), plus(0, x1)), A__ISNAT(plus(0, x1))) A__PLUS(plus(plus(z0, z1), x1), 0) -> c11(A__U11(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), plus(plus(z0, z1), x1)), A__ISNAT(plus(plus(z0, z1), x1))) A__PLUS(plus(s(z0), x1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(x1)), plus(s(z0), x1)), A__ISNAT(plus(s(z0), x1))) A__PLUS(plus(z0, x1), 0) -> c11(A__U11(a__and(isNat(z0), isNat(x1)), plus(z0, x1)), A__ISNAT(plus(z0, x1))) A__PLUS(plus(x0, x1), 0) -> c11(A__ISNAT(plus(x0, x1))) A__PLUS(s(0), 0) -> c11(A__U11(tt, s(0)), A__ISNAT(s(0))) A__PLUS(s(plus(z0, z1)), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__PLUS(s(s(z0)), 0) -> c11(A__U11(a__isNat(z0), s(s(z0))), A__ISNAT(s(s(z0)))) A__PLUS(s(z0), 0) -> c11(A__ISNAT(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__U21(a__and(and(a__isNat(x1), isNat(x2)), isNat(x0)), plus(x1, x2), x0), A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(plus(0, x2))) -> c12(A__U21(a__and(a__and(tt, isNat(x2)), isNat(x0)), plus(0, x2), x0), A__AND(a__isNat(plus(0, x2)), isNat(x0)), A__ISNAT(plus(0, x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c12(A__U21(a__and(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x2)), isNat(x0)), plus(plus(z0, z1), x2), x0), A__AND(a__isNat(plus(plus(z0, z1), x2)), isNat(x0)), A__ISNAT(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(x2)), isNat(x0)), plus(s(z0), x2), x0), A__AND(a__isNat(plus(s(z0), x2)), isNat(x0)), A__ISNAT(plus(s(z0), x2))) A__PLUS(x0, s(plus(z0, x2))) -> c12(A__U21(a__and(a__and(isNat(z0), isNat(x2)), isNat(x0)), plus(z0, x2), x0), A__AND(a__isNat(plus(z0, x2)), isNat(x0)), A__ISNAT(plus(z0, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> 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mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__ISNAT(plus(x0, x1))) A__ISNAT(plus(s(0), x1)) -> c8(A__AND(tt, isNat(x1)), A__ISNAT(s(0))) A__ISNAT(plus(s(plus(z0, z1)), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(s(plus(z0, z1)))) A__ISNAT(plus(s(s(z0)), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(s(z0)))) A__ISNAT(plus(s(z0), x1)) -> c8(A__ISNAT(s(z0))) A__PLUS(plus(0, x1), 0) -> c11(A__U11(a__and(tt, isNat(x1)), plus(0, x1)), A__ISNAT(plus(0, x1))) A__PLUS(plus(plus(z0, z1), x1), 0) -> c11(A__U11(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), plus(plus(z0, z1), x1)), A__ISNAT(plus(plus(z0, z1), x1))) A__PLUS(plus(s(z0), x1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(x1)), plus(s(z0), x1)), A__ISNAT(plus(s(z0), x1))) A__PLUS(plus(z0, x1), 0) -> c11(A__U11(a__and(isNat(z0), isNat(x1)), plus(z0, x1)), A__ISNAT(plus(z0, x1))) A__PLUS(plus(x0, x1), 0) -> c11(A__ISNAT(plus(x0, x1))) A__PLUS(s(0), 0) -> c11(A__U11(tt, s(0)), A__ISNAT(s(0))) A__PLUS(s(plus(z0, z1)), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__PLUS(s(s(z0)), 0) -> c11(A__U11(a__isNat(z0), s(s(z0))), A__ISNAT(s(s(z0)))) A__PLUS(s(z0), 0) -> c11(A__ISNAT(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__U21(a__and(and(a__isNat(x1), isNat(x2)), isNat(x0)), plus(x1, x2), x0), A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(plus(0, x2))) -> c12(A__U21(a__and(a__and(tt, isNat(x2)), isNat(x0)), plus(0, x2), x0), A__AND(a__isNat(plus(0, x2)), isNat(x0)), A__ISNAT(plus(0, x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c12(A__U21(a__and(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x2)), isNat(x0)), plus(plus(z0, z1), x2), x0), A__AND(a__isNat(plus(plus(z0, z1), x2)), isNat(x0)), A__ISNAT(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(x2)), isNat(x0)), plus(s(z0), x2), x0), A__AND(a__isNat(plus(s(z0), x2)), isNat(x0)), A__ISNAT(plus(s(z0), x2))) A__PLUS(x0, s(plus(z0, x2))) -> c12(A__U21(a__and(a__and(isNat(z0), isNat(x2)), isNat(x0)), plus(z0, x2), x0), A__AND(a__isNat(plus(z0, x2)), isNat(x0)), A__ISNAT(plus(z0, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_1, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1, c8_2, c11_2, c12_1 ---------------------------------------- (241) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) by A__PLUS(x0, s(s(x1))) -> c12(A__U21(and(a__isNat(x1), isNat(x0)), s(x1), x0), A__AND(a__isNat(s(x1)), isNat(x0)), A__ISNAT(s(x1))) A__PLUS(x0, s(s(0))) -> c12(A__U21(a__and(tt, isNat(x0)), s(0), x0), A__AND(a__isNat(s(0)), isNat(x0)), A__ISNAT(s(0))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), s(plus(z0, z1)), x0), A__AND(a__isNat(s(plus(z0, z1))), isNat(x0)), A__ISNAT(s(plus(z0, z1)))) A__PLUS(x0, s(s(s(z0)))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(s(z0)), x0), A__AND(a__isNat(s(s(z0))), isNat(x0)), A__ISNAT(s(s(z0)))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(s(x1))) -> c12(A__AND(a__isNat(s(x1)), isNat(x0))) ---------------------------------------- (242) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> 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U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__ISNAT(plus(x0, x1))) A__ISNAT(plus(s(0), x1)) -> c8(A__AND(tt, isNat(x1)), A__ISNAT(s(0))) A__ISNAT(plus(s(plus(z0, z1)), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(s(plus(z0, z1)))) A__ISNAT(plus(s(s(z0)), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(s(z0)))) A__ISNAT(plus(s(z0), x1)) -> c8(A__ISNAT(s(z0))) A__PLUS(plus(0, x1), 0) -> c11(A__U11(a__and(tt, isNat(x1)), plus(0, x1)), A__ISNAT(plus(0, x1))) A__PLUS(plus(plus(z0, z1), x1), 0) -> c11(A__U11(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), plus(plus(z0, z1), x1)), A__ISNAT(plus(plus(z0, z1), x1))) A__PLUS(plus(s(z0), x1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(x1)), plus(s(z0), x1)), A__ISNAT(plus(s(z0), x1))) A__PLUS(plus(z0, x1), 0) -> c11(A__U11(a__and(isNat(z0), isNat(x1)), plus(z0, x1)), A__ISNAT(plus(z0, x1))) A__PLUS(plus(x0, x1), 0) -> c11(A__ISNAT(plus(x0, x1))) A__PLUS(s(0), 0) -> c11(A__U11(tt, s(0)), A__ISNAT(s(0))) A__PLUS(s(plus(z0, z1)), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__PLUS(s(s(z0)), 0) -> c11(A__U11(a__isNat(z0), s(s(z0))), A__ISNAT(s(s(z0)))) A__PLUS(s(z0), 0) -> c11(A__ISNAT(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__U21(a__and(and(a__isNat(x1), isNat(x2)), isNat(x0)), plus(x1, x2), x0), A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(plus(0, x2))) -> c12(A__U21(a__and(a__and(tt, isNat(x2)), isNat(x0)), plus(0, x2), x0), A__AND(a__isNat(plus(0, x2)), isNat(x0)), A__ISNAT(plus(0, x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c12(A__U21(a__and(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x2)), isNat(x0)), plus(plus(z0, z1), x2), x0), A__AND(a__isNat(plus(plus(z0, z1), x2)), isNat(x0)), A__ISNAT(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(x2)), isNat(x0)), plus(s(z0), x2), x0), A__AND(a__isNat(plus(s(z0), x2)), isNat(x0)), A__ISNAT(plus(s(z0), x2))) A__PLUS(x0, s(plus(z0, x2))) -> c12(A__U21(a__and(a__and(isNat(z0), isNat(x2)), isNat(x0)), plus(z0, x2), x0), A__AND(a__isNat(plus(z0, x2)), isNat(x0)), A__ISNAT(plus(z0, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(s(x1))) -> c12(A__U21(and(a__isNat(x1), isNat(x0)), s(x1), x0), A__AND(a__isNat(s(x1)), isNat(x0)), A__ISNAT(s(x1))) A__PLUS(x0, s(s(0))) -> c12(A__U21(a__and(tt, isNat(x0)), s(0), x0), A__AND(a__isNat(s(0)), isNat(x0)), A__ISNAT(s(0))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), s(plus(z0, z1)), x0), A__AND(a__isNat(s(plus(z0, z1))), isNat(x0)), A__ISNAT(s(plus(z0, z1)))) A__PLUS(x0, s(s(s(z0)))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(s(z0)), x0), A__AND(a__isNat(s(s(z0))), isNat(x0)), A__ISNAT(s(s(z0)))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(s(x1))) -> c12(A__AND(a__isNat(s(x1)), isNat(x0))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), 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mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, 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mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__ISNAT(plus(x0, x1))) A__ISNAT(plus(s(0), x1)) -> c8(A__AND(tt, isNat(x1)), A__ISNAT(s(0))) A__ISNAT(plus(s(plus(z0, z1)), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(s(plus(z0, z1)))) A__ISNAT(plus(s(s(z0)), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(s(z0)))) A__ISNAT(plus(s(z0), x1)) -> c8(A__ISNAT(s(z0))) A__PLUS(plus(0, x1), 0) -> c11(A__U11(a__and(tt, isNat(x1)), plus(0, x1)), A__ISNAT(plus(0, x1))) A__PLUS(plus(plus(z0, z1), x1), 0) -> c11(A__U11(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), plus(plus(z0, z1), x1)), A__ISNAT(plus(plus(z0, z1), x1))) A__PLUS(plus(s(z0), x1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(x1)), plus(s(z0), x1)), A__ISNAT(plus(s(z0), x1))) A__PLUS(plus(z0, x1), 0) -> c11(A__U11(a__and(isNat(z0), isNat(x1)), plus(z0, x1)), A__ISNAT(plus(z0, x1))) A__PLUS(plus(x0, x1), 0) -> c11(A__ISNAT(plus(x0, x1))) A__PLUS(s(0), 0) -> c11(A__U11(tt, s(0)), A__ISNAT(s(0))) A__PLUS(s(plus(z0, z1)), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__PLUS(s(s(z0)), 0) -> c11(A__U11(a__isNat(z0), s(s(z0))), A__ISNAT(s(s(z0)))) A__PLUS(s(z0), 0) -> c11(A__ISNAT(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__U21(a__and(and(a__isNat(x1), isNat(x2)), isNat(x0)), plus(x1, x2), x0), A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(plus(0, x2))) -> c12(A__U21(a__and(a__and(tt, isNat(x2)), isNat(x0)), plus(0, x2), x0), A__AND(a__isNat(plus(0, x2)), isNat(x0)), A__ISNAT(plus(0, x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c12(A__U21(a__and(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x2)), isNat(x0)), plus(plus(z0, z1), x2), x0), A__AND(a__isNat(plus(plus(z0, z1), x2)), isNat(x0)), A__ISNAT(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(x2)), isNat(x0)), plus(s(z0), x2), x0), A__AND(a__isNat(plus(s(z0), x2)), isNat(x0)), A__ISNAT(plus(s(z0), x2))) A__PLUS(x0, s(plus(z0, x2))) -> c12(A__U21(a__and(a__and(isNat(z0), isNat(x2)), isNat(x0)), plus(z0, x2), x0), A__AND(a__isNat(plus(z0, x2)), isNat(x0)), A__ISNAT(plus(z0, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(s(x1))) -> c12(A__U21(and(a__isNat(x1), isNat(x0)), s(x1), x0), A__AND(a__isNat(s(x1)), isNat(x0)), A__ISNAT(s(x1))) A__PLUS(x0, s(s(0))) -> c12(A__U21(a__and(tt, isNat(x0)), s(0), x0), A__AND(a__isNat(s(0)), isNat(x0)), A__ISNAT(s(0))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), s(plus(z0, z1)), x0), A__AND(a__isNat(s(plus(z0, z1))), isNat(x0)), A__ISNAT(s(plus(z0, z1)))) A__PLUS(x0, s(s(s(z0)))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(s(z0)), x0), A__AND(a__isNat(s(s(z0))), isNat(x0)), A__ISNAT(s(s(z0)))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(s(x1))) -> c12(A__AND(a__isNat(s(x1)), isNat(x0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_1, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1, c8_2, c11_2, c12_1 ---------------------------------------- (243) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (244) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), 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x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> 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plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, 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and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), 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c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__ISNAT(plus(x0, x1))) A__ISNAT(plus(s(0), x1)) -> c8(A__AND(tt, isNat(x1)), A__ISNAT(s(0))) A__ISNAT(plus(s(plus(z0, z1)), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(s(plus(z0, z1)))) A__ISNAT(plus(s(s(z0)), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(s(z0)))) A__ISNAT(plus(s(z0), x1)) -> c8(A__ISNAT(s(z0))) A__PLUS(plus(0, x1), 0) -> c11(A__U11(a__and(tt, isNat(x1)), plus(0, x1)), A__ISNAT(plus(0, x1))) A__PLUS(plus(plus(z0, z1), x1), 0) -> c11(A__U11(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), plus(plus(z0, z1), x1)), A__ISNAT(plus(plus(z0, z1), x1))) A__PLUS(plus(s(z0), x1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(x1)), plus(s(z0), x1)), A__ISNAT(plus(s(z0), x1))) A__PLUS(plus(z0, x1), 0) -> c11(A__U11(a__and(isNat(z0), isNat(x1)), plus(z0, x1)), A__ISNAT(plus(z0, x1))) A__PLUS(plus(x0, x1), 0) -> c11(A__ISNAT(plus(x0, x1))) A__PLUS(s(0), 0) -> c11(A__U11(tt, s(0)), A__ISNAT(s(0))) A__PLUS(s(plus(z0, z1)), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__PLUS(s(s(z0)), 0) -> c11(A__U11(a__isNat(z0), s(s(z0))), A__ISNAT(s(s(z0)))) A__PLUS(s(z0), 0) -> c11(A__ISNAT(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__U21(a__and(and(a__isNat(x1), isNat(x2)), isNat(x0)), plus(x1, x2), x0), A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(plus(0, x2))) -> c12(A__U21(a__and(a__and(tt, isNat(x2)), isNat(x0)), plus(0, x2), x0), A__AND(a__isNat(plus(0, x2)), isNat(x0)), A__ISNAT(plus(0, x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c12(A__U21(a__and(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x2)), isNat(x0)), plus(plus(z0, z1), x2), x0), A__AND(a__isNat(plus(plus(z0, z1), x2)), isNat(x0)), A__ISNAT(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(x2)), isNat(x0)), plus(s(z0), x2), x0), A__AND(a__isNat(plus(s(z0), x2)), isNat(x0)), A__ISNAT(plus(s(z0), x2))) A__PLUS(x0, s(plus(z0, x2))) -> c12(A__U21(a__and(a__and(isNat(z0), isNat(x2)), isNat(x0)), plus(z0, x2), x0), A__AND(a__isNat(plus(z0, x2)), isNat(x0)), A__ISNAT(plus(z0, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(s(0))) -> c12(A__U21(a__and(tt, isNat(x0)), s(0), x0), A__AND(a__isNat(s(0)), isNat(x0)), A__ISNAT(s(0))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), s(plus(z0, z1)), x0), A__AND(a__isNat(s(plus(z0, z1))), isNat(x0)), A__ISNAT(s(plus(z0, z1)))) A__PLUS(x0, s(s(s(z0)))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(s(z0)), x0), A__AND(a__isNat(s(s(z0))), isNat(x0)), A__ISNAT(s(s(z0)))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(s(x1))) -> c12(A__AND(a__isNat(s(x1)), isNat(x0))) A__PLUS(x0, s(s(x1))) -> c12(A__AND(a__isNat(s(x1)), isNat(x0)), A__ISNAT(s(x1))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), 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U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__ISNAT(plus(x0, x1))) A__ISNAT(plus(s(0), x1)) -> c8(A__AND(tt, isNat(x1)), A__ISNAT(s(0))) A__ISNAT(plus(s(plus(z0, z1)), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(s(plus(z0, z1)))) A__ISNAT(plus(s(s(z0)), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(s(z0)))) A__ISNAT(plus(s(z0), x1)) -> c8(A__ISNAT(s(z0))) A__PLUS(plus(0, x1), 0) -> c11(A__U11(a__and(tt, isNat(x1)), plus(0, x1)), A__ISNAT(plus(0, x1))) A__PLUS(plus(plus(z0, z1), x1), 0) -> c11(A__U11(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), plus(plus(z0, z1), x1)), A__ISNAT(plus(plus(z0, z1), x1))) A__PLUS(plus(s(z0), x1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(x1)), plus(s(z0), x1)), A__ISNAT(plus(s(z0), x1))) A__PLUS(plus(z0, x1), 0) -> c11(A__U11(a__and(isNat(z0), isNat(x1)), plus(z0, x1)), A__ISNAT(plus(z0, x1))) A__PLUS(plus(x0, x1), 0) -> c11(A__ISNAT(plus(x0, x1))) A__PLUS(s(0), 0) -> c11(A__U11(tt, s(0)), A__ISNAT(s(0))) A__PLUS(s(plus(z0, z1)), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__PLUS(s(s(z0)), 0) -> c11(A__U11(a__isNat(z0), s(s(z0))), A__ISNAT(s(s(z0)))) A__PLUS(s(z0), 0) -> c11(A__ISNAT(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__U21(a__and(and(a__isNat(x1), isNat(x2)), isNat(x0)), plus(x1, x2), x0), A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(plus(0, x2))) -> c12(A__U21(a__and(a__and(tt, isNat(x2)), isNat(x0)), plus(0, x2), x0), A__AND(a__isNat(plus(0, x2)), isNat(x0)), A__ISNAT(plus(0, x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c12(A__U21(a__and(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x2)), isNat(x0)), plus(plus(z0, z1), x2), x0), A__AND(a__isNat(plus(plus(z0, z1), x2)), isNat(x0)), A__ISNAT(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(x2)), isNat(x0)), plus(s(z0), x2), x0), A__AND(a__isNat(plus(s(z0), x2)), isNat(x0)), A__ISNAT(plus(s(z0), x2))) A__PLUS(x0, s(plus(z0, x2))) -> c12(A__U21(a__and(a__and(isNat(z0), isNat(x2)), isNat(x0)), plus(z0, x2), x0), A__AND(a__isNat(plus(z0, x2)), isNat(x0)), A__ISNAT(plus(z0, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(s(0))) -> c12(A__U21(a__and(tt, isNat(x0)), s(0), x0), A__AND(a__isNat(s(0)), isNat(x0)), A__ISNAT(s(0))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), s(plus(z0, z1)), x0), A__AND(a__isNat(s(plus(z0, z1))), isNat(x0)), A__ISNAT(s(plus(z0, z1)))) A__PLUS(x0, s(s(s(z0)))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(s(z0)), x0), A__AND(a__isNat(s(s(z0))), isNat(x0)), A__ISNAT(s(s(z0)))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(s(x1))) -> c12(A__AND(a__isNat(s(x1)), isNat(x0))) A__PLUS(x0, s(s(x1))) -> c12(A__AND(a__isNat(s(x1)), isNat(x0)), A__ISNAT(s(x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_1, c11_1, c12_3, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1, c8_2, c11_2, c12_1 ---------------------------------------- (245) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(x0, s(z0)) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), z0, x0), A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(z0)) by A__PLUS(x0, s(x1)) -> c12(A__U21(and(isNat(x1), isNat(x0)), x1, x0), A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) ---------------------------------------- (246) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__ISNAT(plus(x0, x1))) A__ISNAT(plus(s(0), x1)) -> c8(A__AND(tt, isNat(x1)), A__ISNAT(s(0))) A__ISNAT(plus(s(plus(z0, z1)), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(s(plus(z0, z1)))) A__ISNAT(plus(s(s(z0)), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(s(z0)))) A__ISNAT(plus(s(z0), x1)) -> c8(A__ISNAT(s(z0))) A__PLUS(plus(0, x1), 0) -> c11(A__U11(a__and(tt, isNat(x1)), plus(0, x1)), A__ISNAT(plus(0, x1))) A__PLUS(plus(plus(z0, z1), x1), 0) -> c11(A__U11(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), plus(plus(z0, z1), x1)), A__ISNAT(plus(plus(z0, z1), x1))) A__PLUS(plus(s(z0), x1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(x1)), plus(s(z0), x1)), A__ISNAT(plus(s(z0), x1))) A__PLUS(plus(z0, x1), 0) -> c11(A__U11(a__and(isNat(z0), isNat(x1)), plus(z0, x1)), A__ISNAT(plus(z0, x1))) A__PLUS(plus(x0, x1), 0) -> c11(A__ISNAT(plus(x0, x1))) A__PLUS(s(0), 0) -> c11(A__U11(tt, s(0)), A__ISNAT(s(0))) A__PLUS(s(plus(z0, z1)), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__PLUS(s(s(z0)), 0) -> c11(A__U11(a__isNat(z0), s(s(z0))), A__ISNAT(s(s(z0)))) A__PLUS(s(z0), 0) -> c11(A__ISNAT(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__U21(a__and(and(a__isNat(x1), isNat(x2)), isNat(x0)), plus(x1, x2), x0), A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(plus(0, x2))) -> c12(A__U21(a__and(a__and(tt, isNat(x2)), isNat(x0)), plus(0, x2), x0), A__AND(a__isNat(plus(0, x2)), isNat(x0)), A__ISNAT(plus(0, x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c12(A__U21(a__and(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x2)), isNat(x0)), plus(plus(z0, z1), x2), x0), A__AND(a__isNat(plus(plus(z0, z1), x2)), isNat(x0)), A__ISNAT(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(x2)), isNat(x0)), plus(s(z0), x2), x0), A__AND(a__isNat(plus(s(z0), x2)), isNat(x0)), A__ISNAT(plus(s(z0), x2))) A__PLUS(x0, s(plus(z0, x2))) -> c12(A__U21(a__and(a__and(isNat(z0), isNat(x2)), isNat(x0)), plus(z0, x2), x0), A__AND(a__isNat(plus(z0, x2)), isNat(x0)), A__ISNAT(plus(z0, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(s(0))) -> c12(A__U21(a__and(tt, isNat(x0)), s(0), x0), A__AND(a__isNat(s(0)), isNat(x0)), A__ISNAT(s(0))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), s(plus(z0, z1)), x0), A__AND(a__isNat(s(plus(z0, z1))), isNat(x0)), A__ISNAT(s(plus(z0, z1)))) A__PLUS(x0, s(s(s(z0)))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(s(z0)), x0), A__AND(a__isNat(s(s(z0))), isNat(x0)), A__ISNAT(s(s(z0)))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(s(x1))) -> c12(A__AND(a__isNat(s(x1)), isNat(x0))) A__PLUS(x0, s(s(x1))) -> c12(A__AND(a__isNat(s(x1)), isNat(x0)), A__ISNAT(s(x1))) A__PLUS(x0, s(x1)) -> c12(A__U21(and(isNat(x1), isNat(x0)), x1, x0), A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), 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c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__ISNAT(plus(x0, x1))) A__ISNAT(plus(s(0), x1)) -> c8(A__AND(tt, isNat(x1)), A__ISNAT(s(0))) A__ISNAT(plus(s(plus(z0, z1)), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(s(plus(z0, z1)))) A__ISNAT(plus(s(s(z0)), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(s(z0)))) A__ISNAT(plus(s(z0), x1)) -> c8(A__ISNAT(s(z0))) A__PLUS(plus(0, x1), 0) -> c11(A__U11(a__and(tt, isNat(x1)), plus(0, x1)), A__ISNAT(plus(0, x1))) A__PLUS(plus(plus(z0, z1), x1), 0) -> c11(A__U11(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), plus(plus(z0, z1), x1)), A__ISNAT(plus(plus(z0, z1), x1))) A__PLUS(plus(s(z0), x1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(x1)), plus(s(z0), x1)), A__ISNAT(plus(s(z0), x1))) A__PLUS(plus(z0, x1), 0) -> c11(A__U11(a__and(isNat(z0), isNat(x1)), plus(z0, x1)), A__ISNAT(plus(z0, x1))) A__PLUS(plus(x0, x1), 0) -> c11(A__ISNAT(plus(x0, x1))) A__PLUS(s(0), 0) -> c11(A__U11(tt, s(0)), A__ISNAT(s(0))) A__PLUS(s(plus(z0, z1)), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__PLUS(s(s(z0)), 0) -> c11(A__U11(a__isNat(z0), s(s(z0))), A__ISNAT(s(s(z0)))) A__PLUS(s(z0), 0) -> c11(A__ISNAT(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__U21(a__and(and(a__isNat(x1), isNat(x2)), isNat(x0)), plus(x1, x2), x0), A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(plus(0, x2))) -> c12(A__U21(a__and(a__and(tt, isNat(x2)), isNat(x0)), plus(0, x2), x0), A__AND(a__isNat(plus(0, x2)), isNat(x0)), A__ISNAT(plus(0, x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c12(A__U21(a__and(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x2)), isNat(x0)), plus(plus(z0, z1), x2), x0), A__AND(a__isNat(plus(plus(z0, z1), x2)), isNat(x0)), A__ISNAT(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(x2)), isNat(x0)), plus(s(z0), x2), x0), A__AND(a__isNat(plus(s(z0), x2)), isNat(x0)), A__ISNAT(plus(s(z0), x2))) A__PLUS(x0, s(plus(z0, x2))) -> c12(A__U21(a__and(a__and(isNat(z0), isNat(x2)), isNat(x0)), plus(z0, x2), x0), A__AND(a__isNat(plus(z0, x2)), isNat(x0)), A__ISNAT(plus(z0, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(s(0))) -> c12(A__U21(a__and(tt, isNat(x0)), s(0), x0), A__AND(a__isNat(s(0)), isNat(x0)), A__ISNAT(s(0))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), s(plus(z0, z1)), x0), A__AND(a__isNat(s(plus(z0, z1))), isNat(x0)), A__ISNAT(s(plus(z0, z1)))) A__PLUS(x0, s(s(s(z0)))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(s(z0)), x0), A__AND(a__isNat(s(s(z0))), isNat(x0)), A__ISNAT(s(s(z0)))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(s(x1))) -> c12(A__AND(a__isNat(s(x1)), isNat(x0))) A__PLUS(x0, s(s(x1))) -> c12(A__AND(a__isNat(s(x1)), isNat(x0)), A__ISNAT(s(x1))) A__PLUS(x0, s(x1)) -> c12(A__U21(and(isNat(x1), isNat(x0)), x1, x0), A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_1, c11_1, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1, c8_2, c11_2, c12_3, c12_1 ---------------------------------------- (247) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (248) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> 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MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), 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mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__ISNAT(plus(x0, x1))) A__ISNAT(plus(s(0), x1)) -> c8(A__AND(tt, isNat(x1)), A__ISNAT(s(0))) A__ISNAT(plus(s(plus(z0, z1)), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(s(plus(z0, z1)))) A__ISNAT(plus(s(s(z0)), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(s(z0)))) A__ISNAT(plus(s(z0), x1)) -> c8(A__ISNAT(s(z0))) A__PLUS(plus(0, x1), 0) -> c11(A__U11(a__and(tt, isNat(x1)), plus(0, x1)), A__ISNAT(plus(0, x1))) A__PLUS(plus(plus(z0, z1), x1), 0) -> c11(A__U11(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), plus(plus(z0, z1), x1)), A__ISNAT(plus(plus(z0, z1), x1))) A__PLUS(plus(s(z0), x1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(x1)), plus(s(z0), x1)), A__ISNAT(plus(s(z0), x1))) A__PLUS(plus(z0, x1), 0) -> c11(A__U11(a__and(isNat(z0), isNat(x1)), plus(z0, x1)), A__ISNAT(plus(z0, x1))) A__PLUS(plus(x0, x1), 0) -> c11(A__ISNAT(plus(x0, x1))) A__PLUS(s(0), 0) -> c11(A__U11(tt, s(0)), A__ISNAT(s(0))) A__PLUS(s(plus(z0, z1)), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__PLUS(s(s(z0)), 0) -> c11(A__U11(a__isNat(z0), s(s(z0))), A__ISNAT(s(s(z0)))) A__PLUS(s(z0), 0) -> c11(A__ISNAT(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__U21(a__and(and(a__isNat(x1), isNat(x2)), isNat(x0)), plus(x1, x2), x0), A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(plus(0, x2))) -> c12(A__U21(a__and(a__and(tt, isNat(x2)), isNat(x0)), plus(0, x2), x0), A__AND(a__isNat(plus(0, x2)), isNat(x0)), A__ISNAT(plus(0, x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c12(A__U21(a__and(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x2)), isNat(x0)), plus(plus(z0, z1), x2), x0), A__AND(a__isNat(plus(plus(z0, z1), x2)), isNat(x0)), A__ISNAT(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(x2)), isNat(x0)), plus(s(z0), x2), x0), A__AND(a__isNat(plus(s(z0), x2)), isNat(x0)), A__ISNAT(plus(s(z0), x2))) A__PLUS(x0, s(plus(z0, x2))) -> c12(A__U21(a__and(a__and(isNat(z0), isNat(x2)), isNat(x0)), plus(z0, x2), x0), A__AND(a__isNat(plus(z0, x2)), isNat(x0)), A__ISNAT(plus(z0, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(s(0))) -> c12(A__U21(a__and(tt, isNat(x0)), s(0), x0), A__AND(a__isNat(s(0)), isNat(x0)), A__ISNAT(s(0))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), s(plus(z0, z1)), x0), A__AND(a__isNat(s(plus(z0, z1))), isNat(x0)), A__ISNAT(s(plus(z0, z1)))) A__PLUS(x0, s(s(s(z0)))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(s(z0)), x0), A__AND(a__isNat(s(s(z0))), isNat(x0)), A__ISNAT(s(s(z0)))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(s(x1))) -> c12(A__AND(a__isNat(s(x1)), isNat(x0))) A__PLUS(x0, s(s(x1))) -> c12(A__AND(a__isNat(s(x1)), isNat(x0)), A__ISNAT(s(x1))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), 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x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) 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c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__ISNAT(plus(x0, x1))) A__ISNAT(plus(s(0), x1)) -> c8(A__AND(tt, isNat(x1)), A__ISNAT(s(0))) A__ISNAT(plus(s(plus(z0, z1)), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(s(plus(z0, z1)))) A__ISNAT(plus(s(s(z0)), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(s(z0)))) A__ISNAT(plus(s(z0), x1)) -> c8(A__ISNAT(s(z0))) A__PLUS(plus(0, x1), 0) -> c11(A__U11(a__and(tt, isNat(x1)), plus(0, x1)), A__ISNAT(plus(0, x1))) A__PLUS(plus(plus(z0, z1), x1), 0) -> c11(A__U11(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), plus(plus(z0, z1), x1)), A__ISNAT(plus(plus(z0, z1), x1))) A__PLUS(plus(s(z0), x1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(x1)), plus(s(z0), x1)), A__ISNAT(plus(s(z0), x1))) A__PLUS(plus(z0, x1), 0) -> c11(A__U11(a__and(isNat(z0), isNat(x1)), plus(z0, x1)), A__ISNAT(plus(z0, x1))) A__PLUS(plus(x0, x1), 0) -> c11(A__ISNAT(plus(x0, x1))) A__PLUS(s(0), 0) -> c11(A__U11(tt, s(0)), A__ISNAT(s(0))) A__PLUS(s(plus(z0, z1)), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__PLUS(s(s(z0)), 0) -> c11(A__U11(a__isNat(z0), s(s(z0))), A__ISNAT(s(s(z0)))) A__PLUS(s(z0), 0) -> c11(A__ISNAT(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__U21(a__and(and(a__isNat(x1), isNat(x2)), isNat(x0)), plus(x1, x2), x0), A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(plus(0, x2))) -> c12(A__U21(a__and(a__and(tt, isNat(x2)), isNat(x0)), plus(0, x2), x0), A__AND(a__isNat(plus(0, x2)), isNat(x0)), A__ISNAT(plus(0, x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c12(A__U21(a__and(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x2)), isNat(x0)), plus(plus(z0, z1), x2), x0), A__AND(a__isNat(plus(plus(z0, z1), x2)), isNat(x0)), A__ISNAT(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(x2)), isNat(x0)), plus(s(z0), x2), x0), A__AND(a__isNat(plus(s(z0), x2)), isNat(x0)), A__ISNAT(plus(s(z0), x2))) A__PLUS(x0, s(plus(z0, x2))) -> c12(A__U21(a__and(a__and(isNat(z0), isNat(x2)), isNat(x0)), plus(z0, x2), x0), A__AND(a__isNat(plus(z0, x2)), isNat(x0)), A__ISNAT(plus(z0, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(s(0))) -> c12(A__U21(a__and(tt, isNat(x0)), s(0), x0), A__AND(a__isNat(s(0)), isNat(x0)), A__ISNAT(s(0))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), s(plus(z0, z1)), x0), A__AND(a__isNat(s(plus(z0, z1))), isNat(x0)), A__ISNAT(s(plus(z0, z1)))) A__PLUS(x0, s(s(s(z0)))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(s(z0)), x0), A__AND(a__isNat(s(s(z0))), isNat(x0)), A__ISNAT(s(s(z0)))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(s(x1))) -> c12(A__AND(a__isNat(s(x1)), isNat(x0))) A__PLUS(x0, s(s(x1))) -> c12(A__AND(a__isNat(s(x1)), isNat(x0)), A__ISNAT(s(x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_1, c11_1, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1, c8_2, c11_2, c12_3, c12_1 ---------------------------------------- (249) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) by A__PLUS(x0, s(0)) -> c12(A__AND(tt, isNat(x0)), A__ISNAT(0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__AND(isNat(z0), isNat(x0)), A__ISNAT(z0)) ---------------------------------------- (250) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__ISNAT(plus(x0, x1))) A__ISNAT(plus(s(0), x1)) -> c8(A__AND(tt, isNat(x1)), A__ISNAT(s(0))) A__ISNAT(plus(s(plus(z0, z1)), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(s(plus(z0, z1)))) A__ISNAT(plus(s(s(z0)), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(s(z0)))) A__ISNAT(plus(s(z0), x1)) -> c8(A__ISNAT(s(z0))) A__PLUS(plus(0, x1), 0) -> c11(A__U11(a__and(tt, isNat(x1)), plus(0, x1)), A__ISNAT(plus(0, x1))) A__PLUS(plus(plus(z0, z1), x1), 0) -> c11(A__U11(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), plus(plus(z0, z1), x1)), A__ISNAT(plus(plus(z0, z1), x1))) A__PLUS(plus(s(z0), x1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(x1)), plus(s(z0), x1)), A__ISNAT(plus(s(z0), x1))) A__PLUS(plus(z0, x1), 0) -> c11(A__U11(a__and(isNat(z0), isNat(x1)), plus(z0, x1)), A__ISNAT(plus(z0, x1))) A__PLUS(plus(x0, x1), 0) -> c11(A__ISNAT(plus(x0, x1))) A__PLUS(s(0), 0) -> c11(A__U11(tt, s(0)), A__ISNAT(s(0))) A__PLUS(s(plus(z0, z1)), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__PLUS(s(s(z0)), 0) -> c11(A__U11(a__isNat(z0), s(s(z0))), A__ISNAT(s(s(z0)))) A__PLUS(s(z0), 0) -> c11(A__ISNAT(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__U21(a__and(and(a__isNat(x1), isNat(x2)), isNat(x0)), plus(x1, x2), x0), A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(plus(0, x2))) -> c12(A__U21(a__and(a__and(tt, isNat(x2)), isNat(x0)), plus(0, x2), x0), A__AND(a__isNat(plus(0, x2)), isNat(x0)), A__ISNAT(plus(0, x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c12(A__U21(a__and(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x2)), isNat(x0)), plus(plus(z0, z1), x2), x0), A__AND(a__isNat(plus(plus(z0, z1), x2)), isNat(x0)), A__ISNAT(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(x2)), isNat(x0)), plus(s(z0), x2), x0), A__AND(a__isNat(plus(s(z0), x2)), isNat(x0)), A__ISNAT(plus(s(z0), x2))) A__PLUS(x0, s(plus(z0, x2))) -> c12(A__U21(a__and(a__and(isNat(z0), isNat(x2)), isNat(x0)), plus(z0, x2), x0), A__AND(a__isNat(plus(z0, x2)), isNat(x0)), A__ISNAT(plus(z0, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(s(0))) -> c12(A__U21(a__and(tt, isNat(x0)), s(0), x0), A__AND(a__isNat(s(0)), isNat(x0)), A__ISNAT(s(0))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), s(plus(z0, z1)), x0), A__AND(a__isNat(s(plus(z0, z1))), isNat(x0)), A__ISNAT(s(plus(z0, z1)))) A__PLUS(x0, s(s(s(z0)))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(s(z0)), x0), A__AND(a__isNat(s(s(z0))), isNat(x0)), A__ISNAT(s(s(z0)))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(s(x1))) -> c12(A__AND(a__isNat(s(x1)), isNat(x0))) A__PLUS(x0, s(s(x1))) -> c12(A__AND(a__isNat(s(x1)), isNat(x0)), A__ISNAT(s(x1))) A__PLUS(x0, s(0)) -> c12(A__AND(tt, isNat(x0)), A__ISNAT(0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__AND(isNat(z0), isNat(x0)), A__ISNAT(z0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> 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x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, 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a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), 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mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__ISNAT(plus(x0, x1))) A__ISNAT(plus(s(0), x1)) -> c8(A__AND(tt, isNat(x1)), A__ISNAT(s(0))) A__ISNAT(plus(s(plus(z0, z1)), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(s(plus(z0, z1)))) A__ISNAT(plus(s(s(z0)), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(s(z0)))) A__ISNAT(plus(s(z0), x1)) -> c8(A__ISNAT(s(z0))) A__PLUS(plus(0, x1), 0) -> c11(A__U11(a__and(tt, isNat(x1)), plus(0, x1)), A__ISNAT(plus(0, x1))) A__PLUS(plus(plus(z0, z1), x1), 0) -> c11(A__U11(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), plus(plus(z0, z1), x1)), A__ISNAT(plus(plus(z0, z1), x1))) A__PLUS(plus(s(z0), x1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(x1)), plus(s(z0), x1)), A__ISNAT(plus(s(z0), x1))) A__PLUS(plus(z0, x1), 0) -> c11(A__U11(a__and(isNat(z0), isNat(x1)), plus(z0, x1)), A__ISNAT(plus(z0, x1))) A__PLUS(plus(x0, x1), 0) -> c11(A__ISNAT(plus(x0, x1))) A__PLUS(s(0), 0) -> c11(A__U11(tt, s(0)), A__ISNAT(s(0))) A__PLUS(s(plus(z0, z1)), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__PLUS(s(s(z0)), 0) -> c11(A__U11(a__isNat(z0), s(s(z0))), A__ISNAT(s(s(z0)))) A__PLUS(s(z0), 0) -> c11(A__ISNAT(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__U21(a__and(and(a__isNat(x1), isNat(x2)), isNat(x0)), plus(x1, x2), x0), A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(plus(0, x2))) -> c12(A__U21(a__and(a__and(tt, isNat(x2)), isNat(x0)), plus(0, x2), x0), A__AND(a__isNat(plus(0, x2)), isNat(x0)), A__ISNAT(plus(0, x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c12(A__U21(a__and(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x2)), isNat(x0)), plus(plus(z0, z1), x2), x0), A__AND(a__isNat(plus(plus(z0, z1), x2)), isNat(x0)), A__ISNAT(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(x2)), isNat(x0)), plus(s(z0), x2), x0), A__AND(a__isNat(plus(s(z0), x2)), isNat(x0)), A__ISNAT(plus(s(z0), x2))) A__PLUS(x0, s(plus(z0, x2))) -> c12(A__U21(a__and(a__and(isNat(z0), isNat(x2)), isNat(x0)), plus(z0, x2), x0), A__AND(a__isNat(plus(z0, x2)), isNat(x0)), A__ISNAT(plus(z0, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(s(0))) -> c12(A__U21(a__and(tt, isNat(x0)), s(0), x0), A__AND(a__isNat(s(0)), isNat(x0)), A__ISNAT(s(0))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), s(plus(z0, z1)), x0), A__AND(a__isNat(s(plus(z0, z1))), isNat(x0)), A__ISNAT(s(plus(z0, z1)))) A__PLUS(x0, s(s(s(z0)))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(s(z0)), x0), A__AND(a__isNat(s(s(z0))), isNat(x0)), A__ISNAT(s(s(z0)))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(s(x1))) -> c12(A__AND(a__isNat(s(x1)), isNat(x0))) A__PLUS(x0, s(s(x1))) -> c12(A__AND(a__isNat(s(x1)), isNat(x0)), A__ISNAT(s(x1))) A__PLUS(x0, s(0)) -> c12(A__AND(tt, isNat(x0)), A__ISNAT(0)) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(z0)) -> c12(A__AND(isNat(z0), isNat(x0)), A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_1, c11_1, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1, c8_2, c11_2, c12_3, c12_1 ---------------------------------------- (251) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (252) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__ISNAT(plus(x0, x1))) A__ISNAT(plus(s(0), x1)) -> c8(A__AND(tt, isNat(x1)), A__ISNAT(s(0))) A__ISNAT(plus(s(plus(z0, z1)), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(s(plus(z0, z1)))) A__ISNAT(plus(s(s(z0)), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(s(z0)))) A__ISNAT(plus(s(z0), x1)) -> c8(A__ISNAT(s(z0))) A__PLUS(plus(0, x1), 0) -> c11(A__U11(a__and(tt, isNat(x1)), plus(0, x1)), A__ISNAT(plus(0, x1))) A__PLUS(plus(plus(z0, z1), x1), 0) -> c11(A__U11(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), plus(plus(z0, z1), x1)), A__ISNAT(plus(plus(z0, z1), x1))) A__PLUS(plus(s(z0), x1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(x1)), plus(s(z0), x1)), A__ISNAT(plus(s(z0), x1))) A__PLUS(plus(z0, x1), 0) -> c11(A__U11(a__and(isNat(z0), isNat(x1)), plus(z0, x1)), A__ISNAT(plus(z0, x1))) A__PLUS(plus(x0, x1), 0) -> c11(A__ISNAT(plus(x0, x1))) A__PLUS(s(0), 0) -> c11(A__U11(tt, s(0)), A__ISNAT(s(0))) A__PLUS(s(plus(z0, z1)), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__PLUS(s(s(z0)), 0) -> c11(A__U11(a__isNat(z0), s(s(z0))), A__ISNAT(s(s(z0)))) A__PLUS(s(z0), 0) -> c11(A__ISNAT(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__U21(a__and(and(a__isNat(x1), isNat(x2)), isNat(x0)), plus(x1, x2), x0), A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(plus(0, x2))) -> c12(A__U21(a__and(a__and(tt, isNat(x2)), isNat(x0)), plus(0, x2), x0), A__AND(a__isNat(plus(0, x2)), isNat(x0)), A__ISNAT(plus(0, x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c12(A__U21(a__and(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x2)), isNat(x0)), plus(plus(z0, z1), x2), x0), A__AND(a__isNat(plus(plus(z0, z1), x2)), isNat(x0)), A__ISNAT(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(x2)), isNat(x0)), plus(s(z0), x2), x0), A__AND(a__isNat(plus(s(z0), x2)), isNat(x0)), A__ISNAT(plus(s(z0), x2))) A__PLUS(x0, s(plus(z0, x2))) -> c12(A__U21(a__and(a__and(isNat(z0), isNat(x2)), isNat(x0)), plus(z0, x2), x0), A__AND(a__isNat(plus(z0, x2)), isNat(x0)), A__ISNAT(plus(z0, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(s(0))) -> c12(A__U21(a__and(tt, isNat(x0)), s(0), x0), A__AND(a__isNat(s(0)), isNat(x0)), A__ISNAT(s(0))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), s(plus(z0, z1)), x0), A__AND(a__isNat(s(plus(z0, z1))), isNat(x0)), A__ISNAT(s(plus(z0, z1)))) A__PLUS(x0, s(s(s(z0)))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(s(z0)), x0), A__AND(a__isNat(s(s(z0))), isNat(x0)), A__ISNAT(s(s(z0)))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(s(x1))) -> c12(A__AND(a__isNat(s(x1)), isNat(x0))) A__PLUS(x0, s(s(x1))) -> c12(A__AND(a__isNat(s(x1)), isNat(x0)), A__ISNAT(s(x1))) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c12(A__AND(tt, isNat(x0))) A__PLUS(x0, s(z0)) -> c12(A__ISNAT(z0)) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, and(x0, x1), 0) -> c2(A__PLUS(0, a__and(mark(x0), x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c2(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(x1)) A__U21(tt, isNat(s(z0)), x1) -> c2(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U21(tt, isNat(x0), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(U21(z0, z1, z2))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U21(tt, isNat(x0), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(and(z0, z1))) A__U21(tt, isNat(x0), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U21(tt, isNat(x0), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U21(tt, isNat(0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(z0), x1) -> c2(MARK(x1)) A__U21(tt, isNat(x0), tt) -> c2(A__PLUS(tt, a__isNat(x0))) A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), 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MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__ISNAT(plus(x0, x1))) A__ISNAT(plus(s(0), x1)) -> c8(A__AND(tt, isNat(x1)), A__ISNAT(s(0))) A__ISNAT(plus(s(plus(z0, z1)), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(s(plus(z0, z1)))) A__ISNAT(plus(s(s(z0)), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(s(z0)))) A__ISNAT(plus(s(z0), x1)) -> c8(A__ISNAT(s(z0))) A__PLUS(plus(0, x1), 0) -> c11(A__U11(a__and(tt, isNat(x1)), plus(0, x1)), A__ISNAT(plus(0, x1))) A__PLUS(plus(plus(z0, z1), x1), 0) -> c11(A__U11(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), plus(plus(z0, z1), x1)), A__ISNAT(plus(plus(z0, z1), x1))) A__PLUS(plus(s(z0), x1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(x1)), plus(s(z0), x1)), A__ISNAT(plus(s(z0), x1))) A__PLUS(plus(z0, x1), 0) -> c11(A__U11(a__and(isNat(z0), isNat(x1)), plus(z0, x1)), A__ISNAT(plus(z0, x1))) A__PLUS(plus(x0, x1), 0) -> c11(A__ISNAT(plus(x0, x1))) A__PLUS(s(0), 0) -> c11(A__U11(tt, s(0)), A__ISNAT(s(0))) A__PLUS(s(plus(z0, z1)), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__PLUS(s(s(z0)), 0) -> c11(A__U11(a__isNat(z0), s(s(z0))), A__ISNAT(s(s(z0)))) A__PLUS(s(z0), 0) -> c11(A__ISNAT(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__U21(a__and(and(a__isNat(x1), isNat(x2)), isNat(x0)), plus(x1, x2), x0), A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(plus(0, x2))) -> c12(A__U21(a__and(a__and(tt, isNat(x2)), isNat(x0)), plus(0, x2), x0), A__AND(a__isNat(plus(0, x2)), isNat(x0)), A__ISNAT(plus(0, x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c12(A__U21(a__and(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x2)), isNat(x0)), plus(plus(z0, z1), x2), x0), A__AND(a__isNat(plus(plus(z0, z1), x2)), isNat(x0)), A__ISNAT(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(x2)), isNat(x0)), plus(s(z0), x2), x0), A__AND(a__isNat(plus(s(z0), x2)), isNat(x0)), A__ISNAT(plus(s(z0), x2))) A__PLUS(x0, s(plus(z0, x2))) -> c12(A__U21(a__and(a__and(isNat(z0), isNat(x2)), isNat(x0)), plus(z0, x2), x0), A__AND(a__isNat(plus(z0, x2)), isNat(x0)), A__ISNAT(plus(z0, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(s(0))) -> c12(A__U21(a__and(tt, isNat(x0)), s(0), x0), A__AND(a__isNat(s(0)), isNat(x0)), A__ISNAT(s(0))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), s(plus(z0, z1)), x0), A__AND(a__isNat(s(plus(z0, z1))), isNat(x0)), A__ISNAT(s(plus(z0, z1)))) A__PLUS(x0, s(s(s(z0)))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(s(z0)), x0), A__AND(a__isNat(s(s(z0))), isNat(x0)), A__ISNAT(s(s(z0)))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(s(x1))) -> c12(A__AND(a__isNat(s(x1)), isNat(x0))) A__PLUS(x0, s(s(x1))) -> c12(A__AND(a__isNat(s(x1)), isNat(x0)), A__ISNAT(s(x1))) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c12(A__AND(tt, isNat(x0))) A__PLUS(x0, s(z0)) -> c12(A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_1, c11_1, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1, c8_2, c11_2, c12_3, c12_1 ---------------------------------------- (253) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(x0, s(0)) -> c12(A__U21(a__and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) by A__PLUS(x0, s(0)) -> c12(A__U21(mark(isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) A__PLUS(x0, s(0)) -> c12(A__U21(and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) A__PLUS(x0, s(0)) -> c12(A__AND(a__isNat(0), isNat(x0))) ---------------------------------------- (254) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), 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MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__ISNAT(plus(x0, x1))) A__ISNAT(plus(s(0), x1)) -> c8(A__AND(tt, isNat(x1)), A__ISNAT(s(0))) A__ISNAT(plus(s(plus(z0, z1)), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(s(plus(z0, z1)))) A__ISNAT(plus(s(s(z0)), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(s(z0)))) A__ISNAT(plus(s(z0), x1)) -> c8(A__ISNAT(s(z0))) A__PLUS(plus(0, x1), 0) -> c11(A__U11(a__and(tt, isNat(x1)), plus(0, x1)), A__ISNAT(plus(0, x1))) A__PLUS(plus(plus(z0, z1), x1), 0) -> c11(A__U11(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), plus(plus(z0, z1), x1)), A__ISNAT(plus(plus(z0, z1), x1))) A__PLUS(plus(s(z0), x1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(x1)), plus(s(z0), x1)), A__ISNAT(plus(s(z0), x1))) A__PLUS(plus(z0, x1), 0) -> c11(A__U11(a__and(isNat(z0), isNat(x1)), plus(z0, x1)), A__ISNAT(plus(z0, x1))) A__PLUS(plus(x0, x1), 0) -> c11(A__ISNAT(plus(x0, x1))) A__PLUS(s(0), 0) -> c11(A__U11(tt, s(0)), A__ISNAT(s(0))) A__PLUS(s(plus(z0, z1)), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__PLUS(s(s(z0)), 0) -> c11(A__U11(a__isNat(z0), s(s(z0))), A__ISNAT(s(s(z0)))) A__PLUS(s(z0), 0) -> c11(A__ISNAT(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__U21(a__and(and(a__isNat(x1), isNat(x2)), isNat(x0)), plus(x1, x2), x0), A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(plus(0, x2))) -> c12(A__U21(a__and(a__and(tt, isNat(x2)), isNat(x0)), plus(0, x2), x0), A__AND(a__isNat(plus(0, x2)), isNat(x0)), A__ISNAT(plus(0, x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c12(A__U21(a__and(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x2)), isNat(x0)), plus(plus(z0, z1), x2), x0), A__AND(a__isNat(plus(plus(z0, z1), x2)), isNat(x0)), A__ISNAT(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(x2)), isNat(x0)), plus(s(z0), x2), x0), A__AND(a__isNat(plus(s(z0), x2)), isNat(x0)), A__ISNAT(plus(s(z0), x2))) A__PLUS(x0, s(plus(z0, x2))) -> c12(A__U21(a__and(a__and(isNat(z0), isNat(x2)), isNat(x0)), plus(z0, x2), x0), A__AND(a__isNat(plus(z0, x2)), isNat(x0)), A__ISNAT(plus(z0, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(s(0))) -> c12(A__U21(a__and(tt, isNat(x0)), s(0), x0), A__AND(a__isNat(s(0)), isNat(x0)), A__ISNAT(s(0))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), s(plus(z0, z1)), x0), A__AND(a__isNat(s(plus(z0, z1))), isNat(x0)), A__ISNAT(s(plus(z0, z1)))) A__PLUS(x0, s(s(s(z0)))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(s(z0)), x0), A__AND(a__isNat(s(s(z0))), isNat(x0)), A__ISNAT(s(s(z0)))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(s(x1))) -> c12(A__AND(a__isNat(s(x1)), isNat(x0))) A__PLUS(x0, s(s(x1))) -> c12(A__AND(a__isNat(s(x1)), isNat(x0)), A__ISNAT(s(x1))) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c12(A__AND(tt, isNat(x0))) A__PLUS(x0, s(z0)) -> c12(A__ISNAT(z0)) A__PLUS(x0, s(0)) -> c12(A__U21(mark(isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) A__PLUS(x0, s(0)) -> c12(A__U21(and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) A__PLUS(x0, s(0)) -> c12(A__AND(a__isNat(0), isNat(x0))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, 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A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1))) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(U11(U21(z0, z1, z2), x1))) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1))) A__U21(tt, U11(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(U11(and(z0, z1), x1))) A__U21(tt, U11(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1))) A__U21(tt, U11(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1))) A__U21(tt, U11(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1))) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2))) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2))) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(U21(and(z0, z1), x1, x2))) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(U21(isNat(z0), x1, x2))) A__U21(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2))) A__U21(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2))) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2))) A__U21(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2))) A__U21(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1)))) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2)))) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1)))) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(plus(x0, and(z0, z1)))) A__U21(tt, plus(x0, isNat(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0)))) A__U21(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt))) A__U21(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0)))) A__U21(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0))) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1))) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1))) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1))) A__U21(tt, plus(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(plus(and(z0, z1), x1))) A__U21(tt, plus(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1))) A__U21(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1))) A__U21(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1))) A__U21(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1))) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__ISNAT(plus(x0, x1))) A__ISNAT(plus(s(0), x1)) -> c8(A__AND(tt, isNat(x1)), A__ISNAT(s(0))) A__ISNAT(plus(s(plus(z0, z1)), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(s(plus(z0, z1)))) A__ISNAT(plus(s(s(z0)), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(s(z0)))) A__ISNAT(plus(s(z0), x1)) -> c8(A__ISNAT(s(z0))) A__PLUS(plus(0, x1), 0) -> c11(A__U11(a__and(tt, isNat(x1)), plus(0, x1)), A__ISNAT(plus(0, x1))) A__PLUS(plus(plus(z0, z1), x1), 0) -> c11(A__U11(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), plus(plus(z0, z1), x1)), A__ISNAT(plus(plus(z0, z1), x1))) A__PLUS(plus(s(z0), x1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(x1)), plus(s(z0), x1)), A__ISNAT(plus(s(z0), x1))) A__PLUS(plus(z0, x1), 0) -> c11(A__U11(a__and(isNat(z0), isNat(x1)), plus(z0, x1)), A__ISNAT(plus(z0, x1))) A__PLUS(plus(x0, x1), 0) -> c11(A__ISNAT(plus(x0, x1))) A__PLUS(s(0), 0) -> c11(A__U11(tt, s(0)), A__ISNAT(s(0))) A__PLUS(s(plus(z0, z1)), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__PLUS(s(s(z0)), 0) -> c11(A__U11(a__isNat(z0), s(s(z0))), A__ISNAT(s(s(z0)))) A__PLUS(s(z0), 0) -> c11(A__ISNAT(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__U21(a__and(and(a__isNat(x1), isNat(x2)), isNat(x0)), plus(x1, x2), x0), A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(plus(0, x2))) -> c12(A__U21(a__and(a__and(tt, isNat(x2)), isNat(x0)), plus(0, x2), x0), A__AND(a__isNat(plus(0, x2)), isNat(x0)), A__ISNAT(plus(0, x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c12(A__U21(a__and(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x2)), isNat(x0)), plus(plus(z0, z1), x2), x0), A__AND(a__isNat(plus(plus(z0, z1), x2)), isNat(x0)), A__ISNAT(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(x2)), isNat(x0)), plus(s(z0), x2), x0), A__AND(a__isNat(plus(s(z0), x2)), isNat(x0)), A__ISNAT(plus(s(z0), x2))) A__PLUS(x0, s(plus(z0, x2))) -> c12(A__U21(a__and(a__and(isNat(z0), isNat(x2)), isNat(x0)), plus(z0, x2), x0), A__AND(a__isNat(plus(z0, x2)), isNat(x0)), A__ISNAT(plus(z0, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(s(0))) -> c12(A__U21(a__and(tt, isNat(x0)), s(0), x0), A__AND(a__isNat(s(0)), isNat(x0)), A__ISNAT(s(0))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), s(plus(z0, z1)), x0), A__AND(a__isNat(s(plus(z0, z1))), isNat(x0)), A__ISNAT(s(plus(z0, z1)))) A__PLUS(x0, s(s(s(z0)))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(s(z0)), x0), A__AND(a__isNat(s(s(z0))), isNat(x0)), A__ISNAT(s(s(z0)))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(s(x1))) -> c12(A__AND(a__isNat(s(x1)), isNat(x0))) A__PLUS(x0, s(s(x1))) -> c12(A__AND(a__isNat(s(x1)), isNat(x0)), A__ISNAT(s(x1))) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c12(A__AND(tt, isNat(x0))) A__PLUS(x0, s(z0)) -> c12(A__ISNAT(z0)) A__PLUS(x0, s(0)) -> c12(A__U21(mark(isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) A__PLUS(x0, s(0)) -> c12(A__U21(and(tt, isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) A__PLUS(x0, s(0)) -> c12(A__AND(a__isNat(0), isNat(x0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_1, c11_1, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1, c8_2, c11_2, c12_3, c12_1 ---------------------------------------- (255) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (256) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> mark(z0) a__U11(z0, z1) -> U11(z0, z1) a__U21(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U21(z0, z1, z2) -> U21(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__and(a__isNat(z0), isNat(z1)) a__isNat(s(z0)) -> a__isNat(z0) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U11(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U21(a__and(a__isNat(z1), isNat(z0)), z1, z0) a__plus(z0, z1) -> plus(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(isNat(z0)) -> a__isNat(z0) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) A__PLUS(x0, s(x1)) -> c12(A__AND(a__isNat(x1), isNat(x0)), A__ISNAT(x1)) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, U11(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U21(tt, U11(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, U11(x0, x1), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1))) A__U21(tt, U11(x0, x1), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U21(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U21(tt, U21(and(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__and(mark(z0), z1), x1, x2)), MARK(x3)) A__U21(tt, U21(isNat(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__isNat(z0), x1, x2)), MARK(x3)) A__U21(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3)) A__U21(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3)) A__U21(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3)) A__U21(tt, U21(x0, x1, x2), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U21(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2))) A__U21(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U21(tt, U21(x0, x1, x2), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__U21(mark(x0), x1, x2)), MARK(and(z0, z1))) A__U21(tt, U21(x0, x1, x2), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__U21(mark(x0), x1, x2)), MARK(isNat(z0))) A__U21(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0))) A__U21(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3)) A__U21(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2))) A__U21(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2))) A__U21(tt, plus(x0, U11(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2)) A__U21(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2)) A__U21(tt, plus(x0, and(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__and(mark(z0), z1))), MARK(x2)) A__U21(tt, plus(x0, isNat(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2)) A__U21(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2)) A__U21(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2)) A__U21(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2)) A__U21(tt, plus(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2)) A__U21(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2)) A__U21(tt, plus(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__and(mark(z0), z1), mark(x1))), MARK(x2)) A__U21(tt, plus(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2)) A__U21(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2)) A__U21(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2)) A__U21(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2)) A__U21(tt, plus(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1))) A__U21(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2))) A__U21(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1))) A__U21(tt, plus(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(and(z0, z1))) A__U21(tt, plus(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0))) A__U21(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0))) A__U21(tt, plus(x0, x1), x2) -> c2(MARK(x2)) A__U21(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1)))) A__U21(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1)))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, and(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, and(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, and(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, and(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__and(tt, x1)), MARK(x2)) A__U21(tt, and(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, and(0, x1), x2) -> c2(A__PLUS(mark(x2), a__and(0, x1)), MARK(x2)) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(U21(z0, z1, z2))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(plus(z0, z1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c2(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(z0, z1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c2(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(isNat(z0))) A__U21(tt, and(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(s(z0))) A__U21(tt, and(x0, z1), x2) -> c2(MARK(x2)) A__U21(tt, and(x0, x1), tt) -> c2(A__PLUS(tt, a__and(mark(x0), x1))) A__U21(tt, 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A__U21(tt, isNat(x0), 0) -> c2(A__PLUS(0, a__isNat(x0))) A__U21(tt, s(z0), U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2))) A__U21(tt, 0, U11(x1, x2)) -> c2(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2))) A__U21(tt, x0, U11(x1, z1)) -> c2(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1))) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2))) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U21(z0, z1, z2), x2))) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2))) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c2(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(U11(and(z0, z1), x2))) A__U21(tt, x0, U11(isNat(z0), x2)) -> c2(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2))) A__U21(tt, x0, U11(tt, x2)) -> c2(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2))) A__U21(tt, x0, U11(s(z0), x2)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2))) A__U21(tt, tt, U11(x1, x2)) -> c2(MARK(U11(x1, x2))) A__U21(tt, x0, U11(0, x2)) -> c2(A__PLUS(a__U11(0, x2), mark(x0))) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3))) A__U21(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2))) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(U11(z0, z1), x2, x3))) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3))) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3))) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(U21(and(z0, z1), x2, x3))) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c2(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(U21(isNat(z0), x2, x3))) A__U21(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3))) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3))) A__U21(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3))) A__U21(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0))) A__U21(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2))) A__U21(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2))) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1)))) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2)))) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1)))) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(plus(x1, and(z0, z1)))) A__U21(tt, x0, plus(x1, isNat(z0))) -> c2(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0)))) A__U21(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt))) A__U21(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0)))) A__U21(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0))) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2))) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2))) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2))) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(and(z0, z1), x2))) A__U21(tt, x0, plus(isNat(z0), x2)) -> c2(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2))) A__U21(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2))) A__U21(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2))) A__U21(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2))) A__U21(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2))) A__U21(tt, s(z0), and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(and(x1, x2))) A__U21(tt, 0, and(x1, x2)) -> c2(A__PLUS(a__and(mark(x1), x2), 0), MARK(and(x1, x2))) A__U21(tt, x0, and(x1, z1)) -> c2(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(and(x1, z1))) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c2(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(and(U11(z0, z1), x2))) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(and(U21(z0, z1, z2), x2))) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c2(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(and(plus(z0, z1), x2))) A__U21(tt, x0, and(and(z0, z1), x2)) -> c2(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(and(and(z0, z1), x2))) A__U21(tt, x0, and(isNat(z0), x2)) -> c2(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(and(isNat(z0), x2))) A__U21(tt, x0, and(tt, x2)) -> c2(A__PLUS(a__and(tt, x2), mark(x0)), MARK(and(tt, x2))) A__U21(tt, x0, and(s(z0), x2)) -> c2(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(and(s(z0), x2))) A__U21(tt, tt, and(x1, x2)) -> c2(MARK(and(x1, x2))) A__U21(tt, x0, and(0, x2)) -> c2(A__PLUS(a__and(0, x2), mark(x0))) A__U21(tt, s(z0), isNat(x1)) -> c2(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1))) A__U21(tt, 0, isNat(x1)) -> c2(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1))) A__U21(tt, x0, isNat(0)) -> c2(A__PLUS(tt, mark(x0)), MARK(isNat(0))) A__U21(tt, x0, isNat(plus(z0, z1))) -> c2(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(isNat(plus(z0, z1)))) A__U21(tt, x0, isNat(s(z0))) -> c2(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(s(z0)))) A__U21(tt, x0, isNat(z0)) -> c2(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0))) A__U21(tt, tt, isNat(x1)) -> c2(MARK(isNat(x1))) A__U21(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1))) A__U21(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1))) A__U21(tt, x0, s(U11(z0, z1))) -> c2(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1)))) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2)))) A__U21(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1)))) A__U21(tt, x0, s(and(z0, z1))) -> c2(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(s(and(z0, z1)))) A__U21(tt, x0, s(isNat(z0))) -> c2(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0)))) A__U21(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt))) A__U21(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0)))) A__U21(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0))) A__U21(tt, x0, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, tt, s(x1)) -> c2(MARK(s(x1))) A__U21(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0)))) A__U21(tt, 0, tt) -> c2(A__PLUS(tt, 0)) A__U21(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0)))) A__U21(tt, 0, 0) -> c2(A__PLUS(0, 0)) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), 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A__U21(tt, U11(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, x1), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1))) A__U21(tt, U11(x0, z1), x2) -> c3(MARK(U11(x0, z1))) A__U21(tt, U11(0, x1), x2) -> c3(A__PLUS(mark(x2), a__U11(0, x1))) A__U21(tt, U21(U11(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1), x1, x2)), MARK(U21(U11(z0, z1), x1, x2))) A__U21(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), 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mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__ISNAT(plus(x0, x1))) A__ISNAT(plus(s(0), x1)) -> c8(A__AND(tt, isNat(x1)), A__ISNAT(s(0))) A__ISNAT(plus(s(plus(z0, z1)), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(s(plus(z0, z1)))) A__ISNAT(plus(s(s(z0)), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(s(z0)))) A__ISNAT(plus(s(z0), x1)) -> c8(A__ISNAT(s(z0))) A__PLUS(plus(0, x1), 0) -> c11(A__U11(a__and(tt, isNat(x1)), plus(0, x1)), A__ISNAT(plus(0, x1))) A__PLUS(plus(plus(z0, z1), x1), 0) -> c11(A__U11(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), plus(plus(z0, z1), x1)), A__ISNAT(plus(plus(z0, z1), x1))) A__PLUS(plus(s(z0), x1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(x1)), plus(s(z0), x1)), A__ISNAT(plus(s(z0), x1))) A__PLUS(plus(z0, x1), 0) -> c11(A__U11(a__and(isNat(z0), isNat(x1)), plus(z0, x1)), A__ISNAT(plus(z0, x1))) A__PLUS(plus(x0, x1), 0) -> c11(A__ISNAT(plus(x0, x1))) A__PLUS(s(0), 0) -> c11(A__U11(tt, s(0)), A__ISNAT(s(0))) A__PLUS(s(plus(z0, z1)), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__PLUS(s(s(z0)), 0) -> c11(A__U11(a__isNat(z0), s(s(z0))), A__ISNAT(s(s(z0)))) A__PLUS(s(z0), 0) -> c11(A__ISNAT(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__U21(a__and(and(a__isNat(x1), isNat(x2)), isNat(x0)), plus(x1, x2), x0), A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(plus(0, x2))) -> c12(A__U21(a__and(a__and(tt, isNat(x2)), isNat(x0)), plus(0, x2), x0), A__AND(a__isNat(plus(0, x2)), isNat(x0)), A__ISNAT(plus(0, x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c12(A__U21(a__and(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x2)), isNat(x0)), plus(plus(z0, z1), x2), x0), A__AND(a__isNat(plus(plus(z0, z1), x2)), isNat(x0)), A__ISNAT(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(x2)), isNat(x0)), plus(s(z0), x2), x0), A__AND(a__isNat(plus(s(z0), x2)), isNat(x0)), A__ISNAT(plus(s(z0), x2))) A__PLUS(x0, s(plus(z0, x2))) -> c12(A__U21(a__and(a__and(isNat(z0), isNat(x2)), isNat(x0)), plus(z0, x2), x0), A__AND(a__isNat(plus(z0, x2)), isNat(x0)), A__ISNAT(plus(z0, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(s(0))) -> c12(A__U21(a__and(tt, isNat(x0)), s(0), x0), A__AND(a__isNat(s(0)), isNat(x0)), A__ISNAT(s(0))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), s(plus(z0, z1)), x0), A__AND(a__isNat(s(plus(z0, z1))), isNat(x0)), A__ISNAT(s(plus(z0, z1)))) A__PLUS(x0, s(s(s(z0)))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(s(z0)), x0), A__AND(a__isNat(s(s(z0))), isNat(x0)), A__ISNAT(s(s(z0)))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(s(x1))) -> c12(A__AND(a__isNat(s(x1)), isNat(x0))) A__PLUS(x0, s(s(x1))) -> c12(A__AND(a__isNat(s(x1)), isNat(x0)), A__ISNAT(s(x1))) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c12(A__AND(tt, isNat(x0))) A__PLUS(x0, s(z0)) -> c12(A__ISNAT(z0)) A__PLUS(x0, s(0)) -> c12(A__U21(mark(isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) A__PLUS(x0, s(0)) -> c12(A__AND(a__isNat(0), isNat(x0))) S tuples: A__U11(tt, z0) -> c(MARK(z0)) A__AND(tt, z0) -> c5(MARK(z0)) A__ISNAT(s(z0)) -> c9(A__ISNAT(z0)) MARK(isNat(z0)) -> c19(A__ISNAT(z0)) MARK(s(z0)) -> c21(MARK(z0)) A__U21(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U21(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1)) A__U21(tt, tt, x1) -> c2(MARK(x1)) A__U21(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0)) A__ISNAT(plus(0, x1)) -> c8(A__AND(tt, isNat(x1))) A__ISNAT(plus(z0, x1)) -> c8(A__ISNAT(z0)) A__PLUS(0, 0) -> c11(A__U11(tt, 0)) A__PLUS(z0, 0) -> c11(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c14(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U21(z0, z1, z2), x1)) -> c14(A__U11(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c14(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(and(z0, z1), x1)) -> c14(A__U11(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(U11(isNat(z0), x1)) -> c14(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(tt, x1)) -> c14(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c14(MARK(s(z0))) MARK(U21(U11(z0, z1), x1, x2)) -> c15(A__U21(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U21(U21(z0, z1, z2), x1, x2)) -> c15(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2))) MARK(U21(plus(z0, z1), x1, x2)) -> c15(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U21(and(z0, z1), x1, x2)) -> c15(A__U21(a__and(mark(z0), z1), x1, x2), MARK(and(z0, z1))) MARK(U21(isNat(z0), x1, x2)) -> c15(A__U21(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U21(tt, x1, x2)) -> c15(A__U21(tt, x1, x2)) MARK(U21(s(z0), x1, x2)) -> c15(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c16(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U21(z0, z1, z2))) -> c16(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c16(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c16(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c16(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, s(z0))) -> c16(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c16(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c16(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U21(z0, z1, z2), x1)) -> c16(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c16(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(and(z0, z1), x1)) -> c16(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(isNat(z0), x1)) -> c16(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(s(z0), x1)) -> c16(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c16(MARK(x0)) MARK(plus(tt, x1)) -> c16(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c16(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c17(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U21(z0, z1, z2))) -> c17(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c17(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, and(z0, z1))) -> c17(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, isNat(z0))) -> c17(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, s(z0))) -> c17(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c17(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U21(z0, z1, z2), x1)) -> c17(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c17(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(and(z0, z1), x1)) -> c17(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c17(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c17(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c17(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c17(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c17(A__PLUS(mark(x0), 0)) MARK(and(U11(z0, z1), x1)) -> c18(A__AND(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(and(U21(z0, z1, z2), x1)) -> c18(A__AND(a__U21(mark(z0), z1, z2), x1), MARK(U21(z0, z1, z2))) MARK(and(plus(z0, z1), x1)) -> c18(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(and(z0, z1), x1)) -> c18(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(isNat(z0), x1)) -> c18(A__AND(a__isNat(z0), x1), MARK(isNat(z0))) MARK(and(tt, x1)) -> c18(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c18(MARK(s(z0))) A__U21(tt, U11(U11(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__U21(mark(z0), z1, z2), x1)), MARK(x2)) A__U21(tt, U11(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U21(tt, U11(and(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__and(mark(z0), z1), x1)), MARK(x2)) A__U21(tt, U11(isNat(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U21(tt, U11(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U21(tt, U11(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U21(tt, U11(0, x1), x2) -> c2(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U21(tt, U11(x0, x1), U11(z0, z1)) -> c2(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U21(tt, U11(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), 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plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1))) A__U21(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1))) A__U21(tt, and(U11(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U11(mark(z0), z1), x1)), MARK(and(U11(z0, z1), x1))) A__U21(tt, and(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__U21(mark(z0), z1, z2), x1)), MARK(and(U21(z0, z1, z2), x1))) A__U21(tt, and(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__plus(mark(z0), mark(z1)), x1)), MARK(and(plus(z0, z1), x1))) A__U21(tt, and(and(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__and(mark(z0), z1), x1)), MARK(and(and(z0, z1), x1))) A__U21(tt, and(isNat(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(a__isNat(z0), x1)), MARK(and(isNat(z0), x1))) A__U21(tt, and(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__and(tt, x1)), MARK(and(tt, x1))) A__U21(tt, and(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__and(s(mark(z0)), x1)), MARK(and(s(z0), x1))) A__U21(tt, and(x0, x1), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), tt) -> c3(A__PLUS(tt, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, x1), 0) -> c3(A__PLUS(0, a__and(mark(x0), x1)), MARK(and(x0, x1))) A__U21(tt, and(x0, z1), x2) -> c3(MARK(and(x0, z1))) A__U21(tt, and(0, x1), x2) -> c3(A__PLUS(mark(x2), a__and(0, x1))) A__U21(tt, isNat(plus(z0, z1)), x1) -> c3(A__PLUS(mark(x1), a__and(a__isNat(z0), isNat(z1))), MARK(isNat(plus(z0, z1)))) A__U21(tt, isNat(s(z0)), x1) -> c3(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(s(z0)))) A__U21(tt, isNat(x0), U11(z0, z1)) -> c3(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), and(z0, z1)) -> c3(A__PLUS(a__and(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), isNat(z0)) -> c3(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), tt) -> c3(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(x0), 0) -> c3(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0))) A__U21(tt, isNat(0), x1) -> c3(MARK(isNat(0))) A__U21(tt, isNat(z0), x1) -> c3(MARK(isNat(z0))) A__U21(tt, s(z0), U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U11(x1, z1)) -> c3(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U11(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(plus(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(and(z0, z1), x2)) -> c3(A__PLUS(a__U11(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(isNat(z0), x2)) -> c3(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(tt, x2)) -> c3(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(s(z0), x2)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, U11(0, x2)) -> c3(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, U11(x1, x2)) -> c3(A__PLUS(a__U11(mark(x1), x2), 0)) A__U21(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U11(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(and(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__and(mark(z0), z1), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(isNat(z0), x2, x3)) -> c3(A__PLUS(a__U21(a__isNat(z0), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0)) A__U21(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0)) A__U21(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0)) A__U21(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U11(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, isNat(z0))) -> c3(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U11(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(and(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(isNat(z0), x2)) -> c3(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0)) A__U21(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0)) A__U21(tt, s(z0), and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, and(x1, z1)) -> c3(A__PLUS(and(mark(x1), z1), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U11(z0, z1), x2)) -> c3(A__PLUS(a__and(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__and(a__U21(mark(z0), z1, z2), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(plus(z0, z1), x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(and(z0, z1), x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(isNat(z0), x2)) -> c3(A__PLUS(a__and(a__isNat(z0), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(tt, x2)) -> c3(A__PLUS(a__and(tt, x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(s(z0), x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x2), mark(x0)), MARK(x0)) A__U21(tt, x0, and(0, x2)) -> c3(A__PLUS(a__and(0, x2), mark(x0)), MARK(x0)) A__U21(tt, 0, and(x1, x2)) -> c3(A__PLUS(a__and(mark(x1), x2), 0)) A__U21(tt, s(z0), isNat(x1)) -> c3(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, isNat(0)) -> c3(A__PLUS(tt, mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(plus(z0, z1))) -> c3(A__PLUS(a__and(a__isNat(z0), isNat(z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(s(z0))) -> c3(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, x0, isNat(z0)) -> c3(A__PLUS(isNat(z0), mark(x0)), MARK(x0)) A__U21(tt, 0, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), 0)) A__U21(tt, s(z0), tt) -> c3(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, tt) -> c3(A__PLUS(tt, 0)) A__U21(tt, s(z0), s(x1)) -> c3(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(z0))) A__U21(tt, x0, s(U11(z0, z1))) -> c3(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(U21(z0, z1, z2))) -> c3(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(plus(z0, z1))) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(and(z0, z1))) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(isNat(z0))) -> c3(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(x0)) A__U21(tt, x0, s(tt)) -> c3(A__PLUS(s(tt), mark(x0)), MARK(x0)) A__U21(tt, x0, s(s(z0))) -> c3(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(x0)) A__U21(tt, x0, s(0)) -> c3(A__PLUS(s(0), mark(x0)), MARK(x0)) A__U21(tt, 0, s(x1)) -> c3(A__PLUS(s(mark(x1)), 0)) A__U21(tt, s(z0), 0) -> c3(A__PLUS(0, s(mark(z0))), MARK(s(z0))) A__U21(tt, 0, 0) -> c3(A__PLUS(0, 0)) A__ISNAT(plus(plus(0, x1), x2)) -> c8(A__AND(a__and(tt, isNat(x1)), isNat(x2)), A__ISNAT(plus(0, x1))) A__ISNAT(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__AND(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), isNat(x2)), A__ISNAT(plus(plus(z0, z1), x1))) A__ISNAT(plus(plus(s(z0), x1), x2)) -> c8(A__AND(a__and(a__isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(s(z0), x1))) A__ISNAT(plus(plus(z0, x1), x2)) -> c8(A__AND(a__and(isNat(z0), isNat(x1)), isNat(x2)), A__ISNAT(plus(z0, x1))) A__ISNAT(plus(plus(x0, x1), x2)) -> c8(A__ISNAT(plus(x0, x1))) A__ISNAT(plus(s(0), x1)) -> c8(A__AND(tt, isNat(x1)), A__ISNAT(s(0))) A__ISNAT(plus(s(plus(z0, z1)), x1)) -> c8(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), A__ISNAT(s(plus(z0, z1)))) A__ISNAT(plus(s(s(z0)), x1)) -> c8(A__AND(a__isNat(z0), isNat(x1)), A__ISNAT(s(s(z0)))) A__ISNAT(plus(s(z0), x1)) -> c8(A__ISNAT(s(z0))) A__PLUS(plus(0, x1), 0) -> c11(A__U11(a__and(tt, isNat(x1)), plus(0, x1)), A__ISNAT(plus(0, x1))) A__PLUS(plus(plus(z0, z1), x1), 0) -> c11(A__U11(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x1)), plus(plus(z0, z1), x1)), A__ISNAT(plus(plus(z0, z1), x1))) A__PLUS(plus(s(z0), x1), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(x1)), plus(s(z0), x1)), A__ISNAT(plus(s(z0), x1))) A__PLUS(plus(z0, x1), 0) -> c11(A__U11(a__and(isNat(z0), isNat(x1)), plus(z0, x1)), A__ISNAT(plus(z0, x1))) A__PLUS(plus(x0, x1), 0) -> c11(A__ISNAT(plus(x0, x1))) A__PLUS(s(0), 0) -> c11(A__U11(tt, s(0)), A__ISNAT(s(0))) A__PLUS(s(plus(z0, z1)), 0) -> c11(A__U11(a__and(a__isNat(z0), isNat(z1)), s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__PLUS(s(s(z0)), 0) -> c11(A__U11(a__isNat(z0), s(s(z0))), A__ISNAT(s(s(z0)))) A__PLUS(s(z0), 0) -> c11(A__ISNAT(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__U21(a__and(and(a__isNat(x1), isNat(x2)), isNat(x0)), plus(x1, x2), x0), A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(plus(0, x2))) -> c12(A__U21(a__and(a__and(tt, isNat(x2)), isNat(x0)), plus(0, x2), x0), A__AND(a__isNat(plus(0, x2)), isNat(x0)), A__ISNAT(plus(0, x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c12(A__U21(a__and(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x2)), isNat(x0)), plus(plus(z0, z1), x2), x0), A__AND(a__isNat(plus(plus(z0, z1), x2)), isNat(x0)), A__ISNAT(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(x2)), isNat(x0)), plus(s(z0), x2), x0), A__AND(a__isNat(plus(s(z0), x2)), isNat(x0)), A__ISNAT(plus(s(z0), x2))) A__PLUS(x0, s(plus(z0, x2))) -> c12(A__U21(a__and(a__and(isNat(z0), isNat(x2)), isNat(x0)), plus(z0, x2), x0), A__AND(a__isNat(plus(z0, x2)), isNat(x0)), A__ISNAT(plus(z0, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0))) A__PLUS(x0, s(plus(x1, x2))) -> c12(A__AND(a__isNat(plus(x1, x2)), isNat(x0)), A__ISNAT(plus(x1, x2))) A__PLUS(x0, s(s(0))) -> c12(A__U21(a__and(tt, isNat(x0)), s(0), x0), A__AND(a__isNat(s(0)), isNat(x0)), A__ISNAT(s(0))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c12(A__U21(a__and(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), s(plus(z0, z1)), x0), A__AND(a__isNat(s(plus(z0, z1))), isNat(x0)), A__ISNAT(s(plus(z0, z1)))) A__PLUS(x0, s(s(s(z0)))) -> c12(A__U21(a__and(a__isNat(z0), isNat(x0)), s(s(z0)), x0), A__AND(a__isNat(s(s(z0))), isNat(x0)), A__ISNAT(s(s(z0)))) A__PLUS(x0, s(s(z0))) -> c12(A__U21(a__and(isNat(z0), isNat(x0)), s(z0), x0), A__AND(a__isNat(s(z0)), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(s(x1))) -> c12(A__AND(a__isNat(s(x1)), isNat(x0))) A__PLUS(x0, s(s(x1))) -> c12(A__AND(a__isNat(s(x1)), isNat(x0)), A__ISNAT(s(x1))) A__PLUS(x0, s(plus(z0, z1))) -> c12(A__AND(a__and(a__isNat(z0), isNat(z1)), isNat(x0)), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c12(A__AND(a__isNat(z0), isNat(x0)), A__ISNAT(s(z0))) A__PLUS(x0, s(0)) -> c12(A__AND(tt, isNat(x0))) A__PLUS(x0, s(z0)) -> c12(A__ISNAT(z0)) A__PLUS(x0, s(0)) -> c12(A__U21(mark(isNat(x0)), 0, x0), A__AND(a__isNat(0), isNat(x0))) A__PLUS(x0, s(0)) -> c12(A__AND(a__isNat(0), isNat(x0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U21_3, a__and_2, a__isNat_1, a__plus_2, mark_1 Defined Pair Symbols: A__U11_2, A__AND_2, A__ISNAT_1, MARK_1, A__U21_3, A__PLUS_2 Compound Symbols: c_1, c5_1, c9_1, c19_1, c21_1, c2_2, c2_1, c3_2, c3_1, c8_1, c11_1, c12_2, c14_2, c14_1, c15_2, c15_1, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1, c8_2, c11_2, c12_3, c12_1 ---------------------------------------- (257) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (258) 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, N) -> mark(N) [1] a__U21(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__and(a__isNat(V1), isNat(V2)) [1] a__isNat(s(V1)) -> a__isNat(V1) [1] a__plus(N, 0) -> a__U11(a__isNat(N), N) [1] a__plus(N, s(M)) -> a__U21(a__and(a__isNat(M), isNat(N)), M, N) [1] mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1] mark(U21(X1, X2, X3)) -> a__U21(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(isNat(X)) -> a__isNat(X) [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] a__U11(X1, X2) -> U11(X1, X2) [1] a__U21(X1, X2, X3) -> U21(X1, X2, X3) [1] a__plus(X1, X2) -> plus(X1, X2) [1] a__and(X1, X2) -> and(X1, X2) [1] a__isNat(X) -> isNat(X) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (259) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (260) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__U11(tt, N) -> mark(N) [1] a__U21(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__and(a__isNat(V1), isNat(V2)) [1] a__isNat(s(V1)) -> a__isNat(V1) [1] a__plus(N, 0) -> a__U11(a__isNat(N), N) [1] a__plus(N, s(M)) -> a__U21(a__and(a__isNat(M), isNat(N)), M, N) [1] mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1] mark(U21(X1, X2, X3)) -> a__U21(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(isNat(X)) -> a__isNat(X) [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] a__U11(X1, X2) -> U11(X1, X2) [1] a__U21(X1, X2, X3) -> U21(X1, X2, X3) [1] a__plus(X1, X2) -> plus(X1, X2) [1] a__and(X1, X2) -> and(X1, X2) [1] a__isNat(X) -> isNat(X) [1] The TRS has the following type information: a__U11 :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and tt :: tt:s:0:plus:isNat:U11:U21:and mark :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and a__U21 :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and s :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and a__plus :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and a__and :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and a__isNat :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and 0 :: tt:s:0:plus:isNat:U11:U21:and plus :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and isNat :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and U11 :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and U21 :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and and :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and Rewrite Strategy: INNERMOST ---------------------------------------- (261) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: none (c) The following functions are completely defined: a__isNat_1 mark_1 a__and_2 a__U21_3 a__U11_2 a__plus_2 Due to the following rules being added: none And the following fresh constants: none ---------------------------------------- (262) 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, N) -> mark(N) [1] a__U21(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__and(a__isNat(V1), isNat(V2)) [1] a__isNat(s(V1)) -> a__isNat(V1) [1] a__plus(N, 0) -> a__U11(a__isNat(N), N) [1] a__plus(N, s(M)) -> a__U21(a__and(a__isNat(M), isNat(N)), M, N) [1] mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1] mark(U21(X1, X2, X3)) -> a__U21(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(isNat(X)) -> a__isNat(X) [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] a__U11(X1, X2) -> U11(X1, X2) [1] a__U21(X1, X2, X3) -> U21(X1, X2, X3) [1] a__plus(X1, X2) -> plus(X1, X2) [1] a__and(X1, X2) -> and(X1, X2) [1] a__isNat(X) -> isNat(X) [1] The TRS has the following type information: a__U11 :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and tt :: tt:s:0:plus:isNat:U11:U21:and mark :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and a__U21 :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and s :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and a__plus :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and a__and :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and a__isNat :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and 0 :: tt:s:0:plus:isNat:U11:U21:and plus :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and isNat :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and U11 :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and U21 :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and and :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and Rewrite Strategy: INNERMOST ---------------------------------------- (263) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (264) 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, N) -> mark(N) [1] a__U21(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__and(tt, isNat(V2)) [2] a__isNat(plus(plus(V1', V2'), V2)) -> a__and(a__and(a__isNat(V1'), isNat(V2')), isNat(V2)) [2] a__isNat(plus(s(V1''), V2)) -> a__and(a__isNat(V1''), isNat(V2)) [2] a__isNat(plus(V1, V2)) -> a__and(isNat(V1), isNat(V2)) [2] a__isNat(s(V1)) -> a__isNat(V1) [1] a__plus(0, 0) -> a__U11(tt, 0) [2] a__plus(plus(V11, V2''), 0) -> a__U11(a__and(a__isNat(V11), isNat(V2'')), plus(V11, V2'')) [2] a__plus(s(V12), 0) -> a__U11(a__isNat(V12), s(V12)) [2] a__plus(N, 0) -> a__U11(isNat(N), N) [2] a__plus(N, s(0)) -> a__U21(a__and(tt, isNat(N)), 0, N) [2] a__plus(N, s(plus(V13, V21))) -> a__U21(a__and(a__and(a__isNat(V13), isNat(V21)), isNat(N)), plus(V13, V21), N) [2] a__plus(N, s(s(V14))) -> a__U21(a__and(a__isNat(V14), isNat(N)), s(V14), N) [2] a__plus(N, s(M)) -> a__U21(a__and(isNat(M), isNat(N)), M, N) [2] mark(U11(U11(X135, X235), X2)) -> a__U11(a__U11(mark(X135), X235), X2) [2] mark(U11(U21(X136, X236, X311), X2)) -> a__U11(a__U21(mark(X136), X236, X311), X2) [2] mark(U11(plus(X137, X237), X2)) -> a__U11(a__plus(mark(X137), mark(X237)), X2) [2] mark(U11(and(X138, X238), X2)) -> a__U11(a__and(mark(X138), X238), X2) [2] mark(U11(isNat(X44), X2)) -> a__U11(a__isNat(X44), X2) [2] mark(U11(tt, X2)) -> a__U11(tt, X2) [2] mark(U11(s(X45), X2)) -> a__U11(s(mark(X45)), X2) [2] mark(U11(0, X2)) -> a__U11(0, X2) [2] mark(U21(U11(X139, X239), X2, X3)) -> a__U21(a__U11(mark(X139), X239), X2, X3) [2] mark(U21(U21(X140, X240, X312), X2, X3)) -> a__U21(a__U21(mark(X140), X240, X312), X2, X3) [2] mark(U21(plus(X141, X241), X2, X3)) -> a__U21(a__plus(mark(X141), mark(X241)), X2, X3) [2] mark(U21(and(X142, X242), X2, X3)) -> a__U21(a__and(mark(X142), X242), X2, X3) [2] mark(U21(isNat(X46), X2, X3)) -> a__U21(a__isNat(X46), X2, X3) [2] mark(U21(tt, X2, X3)) -> a__U21(tt, X2, X3) [2] mark(U21(s(X47), X2, X3)) -> a__U21(s(mark(X47)), X2, X3) [2] mark(U21(0, X2, X3)) -> a__U21(0, X2, X3) [2] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(and(U11(X179, X279), X2)) -> a__and(a__U11(mark(X179), X279), X2) [2] mark(and(U21(X180, X280, X322), X2)) -> a__and(a__U21(mark(X180), X280, X322), X2) [2] mark(and(plus(X181, X281), X2)) -> a__and(a__plus(mark(X181), mark(X281)), X2) [2] mark(and(and(X182, X282), X2)) -> a__and(a__and(mark(X182), X282), X2) [2] mark(and(isNat(X66), X2)) -> a__and(a__isNat(X66), X2) [2] mark(and(tt, X2)) -> a__and(tt, X2) [2] mark(and(s(X67), X2)) -> a__and(s(mark(X67)), X2) [2] mark(and(0, X2)) -> a__and(0, X2) [2] mark(isNat(X)) -> a__isNat(X) [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] a__U11(X1, X2) -> U11(X1, X2) [1] a__U21(X1, X2, X3) -> U21(X1, X2, X3) [1] a__plus(X1, X2) -> plus(X1, X2) [1] a__and(X1, X2) -> and(X1, X2) [1] a__isNat(X) -> isNat(X) [1] The TRS has the following type information: a__U11 :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and tt :: tt:s:0:plus:isNat:U11:U21:and mark :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and a__U21 :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and s :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and a__plus :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and a__and :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and a__isNat :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and 0 :: tt:s:0:plus:isNat:U11:U21:and plus :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and isNat :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and U11 :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and U21 :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and and :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and Rewrite Strategy: INNERMOST ---------------------------------------- (265) 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 ---------------------------------------- (266) Obligation: Complexity RNTS consisting of the following rules: a__U11(z, z') -{ 1 }-> mark(N) :|: z = 1, z' = N, N >= 0 a__U11(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U21(z, z', z'') -{ 1 }-> 1 + a__plus(mark(N), mark(M)) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U21(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__isNat(V1) :|: z = 1 + V1, V1 >= 0 a__isNat(z) -{ 2 }-> a__and(a__isNat(V1''), 1 + V2) :|: V1'' >= 0, z = 1 + (1 + V1'') + V2, V2 >= 0 a__isNat(z) -{ 2 }-> a__and(a__and(a__isNat(V1'), 1 + V2'), 1 + V2) :|: z = 1 + (1 + V1' + V2') + V2, V2 >= 0, V2' >= 0, V1' >= 0 a__isNat(z) -{ 2 }-> a__and(1, 1 + V2) :|: V2 >= 0, z = 1 + 0 + V2 a__isNat(z) -{ 2 }-> a__and(1 + V1, 1 + V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNat(z) -{ 1 }-> 1 :|: z = 0 a__isNat(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__plus(z, z') -{ 2 }-> a__U21(a__and(a__isNat(V14), 1 + N), 1 + V14, N) :|: V14 >= 0, z' = 1 + (1 + V14), z = N, N >= 0 a__plus(z, z') -{ 2 }-> a__U21(a__and(a__and(a__isNat(V13), 1 + V21), 1 + N), 1 + V13 + V21, N) :|: V21 >= 0, V13 >= 0, z = N, z' = 1 + (1 + V13 + V21), N >= 0 a__plus(z, z') -{ 2 }-> a__U21(a__and(1, 1 + N), 0, N) :|: z = N, z' = 1 + 0, N >= 0 a__plus(z, z') -{ 2 }-> a__U21(a__and(1 + M, 1 + N), M, N) :|: z' = 1 + M, z = N, M >= 0, N >= 0 a__plus(z, z') -{ 2 }-> a__U11(a__isNat(V12), 1 + V12) :|: V12 >= 0, z = 1 + V12, z' = 0 a__plus(z, z') -{ 2 }-> a__U11(a__and(a__isNat(V11), 1 + V2''), 1 + V11 + V2'') :|: V11 >= 0, V2'' >= 0, z = 1 + V11 + V2'', z' = 0 a__plus(z, z') -{ 2 }-> a__U11(1, 0) :|: z = 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U11(1 + N, N) :|: z = N, z' = 0, N >= 0 a__plus(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 mark(z) -{ 1 }-> a__plus(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__isNat(X) :|: z = 1 + X, X >= 0 mark(z) -{ 2 }-> a__and(a__plus(mark(X181), mark(X281)), X2) :|: X181 >= 0, z = 1 + (1 + X181 + X281) + X2, X281 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__isNat(X66), X2) :|: X66 >= 0, X2 >= 0, z = 1 + (1 + X66) + X2 mark(z) -{ 2 }-> a__and(a__and(mark(X182), X282), X2) :|: X282 >= 0, z = 1 + (1 + X182 + X282) + X2, X182 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__U21(mark(X180), X280, X322), X2) :|: X322 >= 0, X280 >= 0, X2 >= 0, X180 >= 0, z = 1 + (1 + X180 + X280 + X322) + X2 mark(z) -{ 2 }-> a__and(a__U11(mark(X179), X279), X2) :|: z = 1 + (1 + X179 + X279) + X2, X279 >= 0, X2 >= 0, X179 >= 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(X67), X2) :|: X67 >= 0, z = 1 + (1 + X67) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__plus(mark(X141), mark(X241)), X2, X3) :|: X3 >= 0, z = 1 + (1 + X141 + X241) + X2 + X3, X241 >= 0, X2 >= 0, X141 >= 0 mark(z) -{ 2 }-> a__U21(a__isNat(X46), X2, X3) :|: X3 >= 0, X46 >= 0, X2 >= 0, z = 1 + (1 + X46) + X2 + X3 mark(z) -{ 2 }-> a__U21(a__and(mark(X142), X242), X2, X3) :|: z = 1 + (1 + X142 + X242) + X2 + X3, X242 >= 0, X3 >= 0, X2 >= 0, X142 >= 0 mark(z) -{ 2 }-> a__U21(a__U21(mark(X140), X240, X312), X2, X3) :|: X240 >= 0, z = 1 + (1 + X140 + X240 + X312) + X2 + X3, X312 >= 0, X3 >= 0, X2 >= 0, X140 >= 0 mark(z) -{ 2 }-> a__U21(a__U11(mark(X139), X239), X2, X3) :|: z = 1 + (1 + X139 + X239) + X2 + X3, X3 >= 0, X239 >= 0, X2 >= 0, X139 >= 0 mark(z) -{ 2 }-> a__U21(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(1 + mark(X47), X2, X3) :|: z = 1 + (1 + X47) + X2 + X3, X47 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__plus(mark(X137), mark(X237)), X2) :|: z = 1 + (1 + X137 + X237) + X2, X137 >= 0, X2 >= 0, X237 >= 0 mark(z) -{ 2 }-> a__U11(a__isNat(X44), X2) :|: z = 1 + (1 + X44) + X2, X2 >= 0, X44 >= 0 mark(z) -{ 2 }-> a__U11(a__and(mark(X138), X238), X2) :|: z = 1 + (1 + X138 + X238) + X2, X2 >= 0, X138 >= 0, X238 >= 0 mark(z) -{ 2 }-> a__U11(a__U21(mark(X136), X236, X311), X2) :|: X311 >= 0, X136 >= 0, X236 >= 0, X2 >= 0, z = 1 + (1 + X136 + X236 + X311) + X2 mark(z) -{ 2 }-> a__U11(a__U11(mark(X135), X235), X2) :|: z = 1 + (1 + X135 + X235) + X2, X135 >= 0, X235 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(1, X2) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(0, X2) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(1 + mark(X45), X2) :|: X45 >= 0, X2 >= 0, z = 1 + (1 + X45) + X2 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 ---------------------------------------- (267) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (268) Obligation: Complexity RNTS consisting of the following rules: a__U11(z, z') -{ 1 }-> mark(z') :|: z = 1, z' >= 0 a__U11(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__U21(z, z', z'') -{ 1 }-> 1 + a__plus(mark(z''), mark(z')) :|: z = 1, z' >= 0, z'' >= 0 a__U21(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) -{ 1 }-> a__isNat(z - 1) :|: z - 1 >= 0 a__isNat(z) -{ 2 }-> a__and(a__isNat(V1''), 1 + V2) :|: V1'' >= 0, z = 1 + (1 + V1'') + V2, V2 >= 0 a__isNat(z) -{ 2 }-> a__and(a__and(a__isNat(V1'), 1 + V2'), 1 + V2) :|: z = 1 + (1 + V1' + V2') + V2, V2 >= 0, V2' >= 0, V1' >= 0 a__isNat(z) -{ 2 }-> a__and(1, 1 + (z - 1)) :|: z - 1 >= 0 a__isNat(z) -{ 2 }-> a__and(1 + V1, 1 + 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__plus(z, z') -{ 2 }-> a__U21(a__and(a__isNat(z' - 2), 1 + z), 1 + (z' - 2), z) :|: z' - 2 >= 0, z >= 0 a__plus(z, z') -{ 2 }-> a__U21(a__and(a__and(a__isNat(V13), 1 + V21), 1 + z), 1 + V13 + V21, z) :|: V21 >= 0, V13 >= 0, z' = 1 + (1 + V13 + V21), z >= 0 a__plus(z, z') -{ 2 }-> a__U21(a__and(1, 1 + z), 0, z) :|: z' = 1 + 0, z >= 0 a__plus(z, z') -{ 2 }-> a__U21(a__and(1 + (z' - 1), 1 + z), z' - 1, z) :|: z' - 1 >= 0, z >= 0 a__plus(z, z') -{ 2 }-> a__U11(a__isNat(z - 1), 1 + (z - 1)) :|: z - 1 >= 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U11(a__and(a__isNat(V11), 1 + V2''), 1 + V11 + V2'') :|: V11 >= 0, V2'' >= 0, z = 1 + V11 + V2'', z' = 0 a__plus(z, z') -{ 2 }-> a__U11(1, 0) :|: z = 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U11(1 + z, z) :|: z' = 0, z >= 0 a__plus(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 mark(z) -{ 1 }-> a__plus(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__isNat(z - 1) :|: z - 1 >= 0 mark(z) -{ 2 }-> a__and(a__plus(mark(X181), mark(X281)), X2) :|: X181 >= 0, z = 1 + (1 + X181 + X281) + X2, X281 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__isNat(X66), X2) :|: X66 >= 0, X2 >= 0, z = 1 + (1 + X66) + X2 mark(z) -{ 2 }-> a__and(a__and(mark(X182), X282), X2) :|: X282 >= 0, z = 1 + (1 + X182 + X282) + X2, X182 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__U21(mark(X180), X280, X322), X2) :|: X322 >= 0, X280 >= 0, X2 >= 0, X180 >= 0, z = 1 + (1 + X180 + X280 + X322) + X2 mark(z) -{ 2 }-> a__and(a__U11(mark(X179), X279), X2) :|: z = 1 + (1 + X179 + X279) + X2, X279 >= 0, X2 >= 0, X179 >= 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(X67), X2) :|: X67 >= 0, z = 1 + (1 + X67) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__plus(mark(X141), mark(X241)), X2, X3) :|: X3 >= 0, z = 1 + (1 + X141 + X241) + X2 + X3, X241 >= 0, X2 >= 0, X141 >= 0 mark(z) -{ 2 }-> a__U21(a__isNat(X46), X2, X3) :|: X3 >= 0, X46 >= 0, X2 >= 0, z = 1 + (1 + X46) + X2 + X3 mark(z) -{ 2 }-> a__U21(a__and(mark(X142), X242), X2, X3) :|: z = 1 + (1 + X142 + X242) + X2 + X3, X242 >= 0, X3 >= 0, X2 >= 0, X142 >= 0 mark(z) -{ 2 }-> a__U21(a__U21(mark(X140), X240, X312), X2, X3) :|: X240 >= 0, z = 1 + (1 + X140 + X240 + X312) + X2 + X3, X312 >= 0, X3 >= 0, X2 >= 0, X140 >= 0 mark(z) -{ 2 }-> a__U21(a__U11(mark(X139), X239), X2, X3) :|: z = 1 + (1 + X139 + X239) + X2 + X3, X3 >= 0, X239 >= 0, X2 >= 0, X139 >= 0 mark(z) -{ 2 }-> a__U21(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U21(1 + mark(X47), X2, X3) :|: z = 1 + (1 + X47) + X2 + X3, X47 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__plus(mark(X137), mark(X237)), X2) :|: z = 1 + (1 + X137 + X237) + X2, X137 >= 0, X2 >= 0, X237 >= 0 mark(z) -{ 2 }-> a__U11(a__isNat(X44), X2) :|: z = 1 + (1 + X44) + X2, X2 >= 0, X44 >= 0 mark(z) -{ 2 }-> a__U11(a__and(mark(X138), X238), X2) :|: z = 1 + (1 + X138 + X238) + X2, X2 >= 0, X138 >= 0, X238 >= 0 mark(z) -{ 2 }-> a__U11(a__U21(mark(X136), X236, X311), X2) :|: X311 >= 0, X136 >= 0, X236 >= 0, X2 >= 0, z = 1 + (1 + X136 + X236 + X311) + X2 mark(z) -{ 2 }-> a__U11(a__U11(mark(X135), X235), X2) :|: z = 1 + (1 + X135 + X235) + X2, X135 >= 0, X235 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(1, z - 2) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U11(0, z - 1) :|: z - 1 >= 0 mark(z) -{ 2 }-> a__U11(1 + mark(X45), X2) :|: X45 >= 0, X2 >= 0, z = 1 + (1 + X45) + X2 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(z - 1) :|: z - 1 >= 0 ---------------------------------------- (269) 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 ---------------------------------------- (270) 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, N) -> mark(N) [1] a__U21(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__and(a__isNat(V1), isNat(V2)) [1] a__isNat(s(V1)) -> a__isNat(V1) [1] a__plus(N, 0) -> a__U11(a__isNat(N), N) [1] a__plus(N, s(M)) -> a__U21(a__and(a__isNat(M), isNat(N)), M, N) [1] mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1] mark(U21(X1, X2, X3)) -> a__U21(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(isNat(X)) -> a__isNat(X) [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] a__U11(X1, X2) -> U11(X1, X2) [1] a__U21(X1, X2, X3) -> U21(X1, X2, X3) [1] a__plus(X1, X2) -> plus(X1, X2) [1] a__and(X1, X2) -> and(X1, X2) [1] a__isNat(X) -> isNat(X) [1] The TRS has the following type information: a__U11 :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and tt :: tt:s:0:plus:isNat:U11:U21:and mark :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and a__U21 :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and s :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and a__plus :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and a__and :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and a__isNat :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and 0 :: tt:s:0:plus:isNat:U11:U21:and plus :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and isNat :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and U11 :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and U21 :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and and :: tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and -> tt:s:0:plus:isNat:U11:U21:and Rewrite Strategy: INNERMOST ---------------------------------------- (271) 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 ---------------------------------------- (272) Obligation: Complexity RNTS consisting of the following rules: a__U11(z, z') -{ 1 }-> mark(N) :|: z = 1, z' = N, N >= 0 a__U11(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U21(z, z', z'') -{ 1 }-> 1 + a__plus(mark(N), mark(M)) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U21(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__isNat(V1) :|: z = 1 + V1, V1 >= 0 a__isNat(z) -{ 1 }-> a__and(a__isNat(V1), 1 + V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNat(z) -{ 1 }-> 1 :|: z = 0 a__isNat(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__plus(z, z') -{ 1 }-> a__U21(a__and(a__isNat(M), 1 + N), M, N) :|: z' = 1 + M, z = N, M >= 0, N >= 0 a__plus(z, z') -{ 1 }-> a__U11(a__isNat(N), N) :|: z = N, z' = 0, N >= 0 a__plus(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 mark(z) -{ 1 }-> a__plus(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__isNat(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__and(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U21(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U11(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 Only complete derivations are relevant for the runtime complexity.