KILLED proof of input_F5bioKvKkD.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) NarrowingProof [BOTH BOUNDS(ID, ID), 27 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 17 ms] (14) CpxRNTS (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxRNTS (17) CompletionProof [UPPER BOUND(ID), 0 ms] (18) CpxTypedWeightedCompleteTrs (19) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (20) CpxRNTS (21) CpxTrsToCdtProof [UPPER BOUND(ID), 1 ms] (22) CdtProblem (23) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (24) CdtProblem (25) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (26) CdtProblem (27) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (28) CdtProblem (29) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CdtProblem (31) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (32) CdtProblem (33) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (34) CdtProblem (35) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (36) CdtProblem (37) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (38) CdtProblem (39) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CdtProblem (41) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CdtProblem (43) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CdtProblem (45) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CdtProblem (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CdtProblem (49) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CdtProblem (51) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CdtProblem (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CdtProblem (55) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CdtProblem (57) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 11 ms] (80) CdtProblem (81) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 5 ms] (88) CdtProblem (89) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 7 ms] (98) CdtProblem (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 32 ms] (104) CdtProblem (105) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (106) CdtProblem (107) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem (111) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9 ms] (116) CdtProblem (117) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9 ms] (120) CdtProblem (121) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (122) CdtProblem (123) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (126) CdtProblem (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (128) CdtProblem (129) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (132) CdtProblem (133) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (134) CdtProblem (135) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (138) CdtProblem (139) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (140) CdtProblem (141) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (144) CdtProblem (145) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (146) CdtProblem (147) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2 ms] (148) CdtProblem (149) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (150) CdtProblem (151) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (152) CdtProblem (153) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 32 ms] (154) CdtProblem (155) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (156) CdtProblem (157) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (158) CdtProblem (159) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 13 ms] (160) CdtProblem (161) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (162) CdtProblem (163) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (164) CdtProblem (165) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 34 ms] (166) CdtProblem (167) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (168) CdtProblem (169) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (170) CdtProblem (171) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 25 ms] (172) CdtProblem (173) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (174) CdtProblem (175) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (176) CdtProblem (177) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 13 ms] (178) CdtProblem (179) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (180) CdtProblem (181) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (182) CdtProblem (183) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4 ms] (184) CdtProblem (185) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (186) CdtProblem (187) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (188) CdtProblem (189) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 25 ms] (190) CdtProblem (191) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (192) CdtProblem (193) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (194) CdtProblem (195) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 12 ms] (196) CdtProblem (197) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (198) CdtProblem (199) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 13 ms] (200) CdtProblem (201) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 6 ms] (202) CdtProblem (203) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 11 ms] (204) CdtProblem (205) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (206) CdtProblem (207) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 39 ms] (208) CdtProblem (209) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 12 ms] (210) CdtProblem (211) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 28 ms] (212) CdtProblem (213) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 7 ms] (214) CdtProblem (215) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 52 ms] (216) CdtProblem (217) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (218) CdtProblem (219) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 19 ms] (220) CdtProblem (221) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (222) CdtProblem (223) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 51 ms] (224) CdtProblem (225) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 12 ms] (226) CdtProblem (227) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 7 ms] (228) CdtProblem (229) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (230) CdtProblem ---------------------------------------- (0) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__U11(tt, 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) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (6) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__U11(tt, 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 ---------------------------------------- (7) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (8) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__U11(tt, 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 ---------------------------------------- (9) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: none (c) The following functions are completely defined: a__isNat_1 mark_1 a__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 ---------------------------------------- (10) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__U11(tt, 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 ---------------------------------------- (11) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (12) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__U11(tt, 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 ---------------------------------------- (13) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: tt => 1 0 => 0 ---------------------------------------- (14) Obligation: Complexity RNTS consisting of the following rules: a__U11(z, z') -{ 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 ---------------------------------------- (15) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (16) 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 ---------------------------------------- (17) 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 ---------------------------------------- (18) 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 ---------------------------------------- (19) 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 ---------------------------------------- (20) 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. ---------------------------------------- (21) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (22) 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 ---------------------------------------- (23) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 8 trailing nodes: A__AND(z0, z1) -> c6 MARK(tt) -> c20 A__ISNAT(0) -> c7 A__U11(z0, z1) -> c1 MARK(0) -> c22 A__U21(z0, z1, z2) -> c4 A__PLUS(z0, z1) -> c13 A__ISNAT(z0) -> c10 ---------------------------------------- (24) 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 ---------------------------------------- (25) 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)) ---------------------------------------- (26) 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 ---------------------------------------- (27) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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__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 ---------------------------------------- (29) 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)) ---------------------------------------- (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__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 ---------------------------------------- (31) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U21(tt, tt, x1) -> c3(A__PLUS(mark(x1), tt), MARK(tt)) ---------------------------------------- (32) 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 ---------------------------------------- (33) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (34) 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 ---------------------------------------- (35) 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)) ---------------------------------------- (36) 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 ---------------------------------------- (37) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (38) 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 ---------------------------------------- (39) 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)) ---------------------------------------- (40) 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 ---------------------------------------- (41) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (42) 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 ---------------------------------------- (43) 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)) ---------------------------------------- (44) 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 ---------------------------------------- (45) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (46) 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 ---------------------------------------- (47) 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)) ---------------------------------------- (48) 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 ---------------------------------------- (49) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U11(0, x1)) -> c14(A__U11(0, x1), MARK(0)) ---------------------------------------- (50) 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 ---------------------------------------- (51) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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__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 ---------------------------------------- (53) 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)) ---------------------------------------- (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__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 ---------------------------------------- (55) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U21(0, x1, x2)) -> c15(A__U21(0, x1, x2), MARK(0)) ---------------------------------------- (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(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 ---------------------------------------- (57) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (59) 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)) ---------------------------------------- (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(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 ---------------------------------------- (61) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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)) 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 ---------------------------------------- (63) 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)) ---------------------------------------- (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)) 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 ---------------------------------------- (65) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(x0, tt)) -> c17(A__PLUS(mark(x0), tt), MARK(tt)) ---------------------------------------- (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)) 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 ---------------------------------------- (67) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 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)) 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 ---------------------------------------- (69) 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)) ---------------------------------------- (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(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 ---------------------------------------- (71) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(and(0, x1)) -> c18(A__AND(0, x1), MARK(0)) ---------------------------------------- (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(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 ---------------------------------------- (73) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (75) 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)) ---------------------------------------- (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(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 ---------------------------------------- (77) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 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(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 ---------------------------------------- (79) 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)) ---------------------------------------- (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(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 ---------------------------------------- (81) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (83) 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)) ---------------------------------------- (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(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 ---------------------------------------- (85) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (87) 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)) ---------------------------------------- (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(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 ---------------------------------------- (89) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (91) 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)) ---------------------------------------- (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(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 ---------------------------------------- (93) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 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(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 ---------------------------------------- (95) 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))) ---------------------------------------- (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, 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 ---------------------------------------- (97) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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, 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))) 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))) 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 ---------------------------------------- (99) 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))) ---------------------------------------- (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, 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), 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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 ---------------------------------------- (101) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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, 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 ---------------------------------------- (103) 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))) ---------------------------------------- (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, 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))), 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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), 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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 ---------------------------------------- (105) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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, 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), 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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)) -> 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))) 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) 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))) ---------------------------------------- (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, 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, 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)), 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))) 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) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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, 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))) 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 ---------------------------------------- (111) 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))) ---------------------------------------- (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, 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, 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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 ---------------------------------------- (113) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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, 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), 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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 ---------------------------------------- (115) 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))) ---------------------------------------- (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, 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 ---------------------------------------- (117) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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, 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))), 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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))) 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 ---------------------------------------- (119) 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)) ---------------------------------------- (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, 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, 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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)) 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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 ---------------------------------------- (121) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U21(tt, tt, tt) -> c2(A__PLUS(tt, tt)) ---------------------------------------- (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, 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)), 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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 ---------------------------------------- (123) 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)) ---------------------------------------- (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, 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)), 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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 ---------------------------------------- (125) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U21(tt, tt, 0) -> c2(A__PLUS(0, tt)) ---------------------------------------- (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, 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)) 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))) 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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))) 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 ---------------------------------------- (127) 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))) ---------------------------------------- (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, 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)), 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)))) 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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(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 ---------------------------------------- (129) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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, 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))) 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) -> 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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))) 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) 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))) ---------------------------------------- (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, 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, 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(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), 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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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 ---------------------------------------- (133) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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, 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), 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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))) 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), 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))) 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) 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))) ---------------------------------------- (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, 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), 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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, 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) -> 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, 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 ---------------------------------------- (137) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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, 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), 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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))) 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) -> 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))), 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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 ---------------------------------------- (139) 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))) ---------------------------------------- (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, 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))) 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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(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)) -> 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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(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 ---------------------------------------- (141) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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, 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, 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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), 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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))) 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) 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))) ---------------------------------------- (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, 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)) -> 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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))), 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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 ---------------------------------------- (145) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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, 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), 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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))) 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) -> 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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 ---------------------------------------- (147) 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)) ---------------------------------------- (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, 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), 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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))) -> 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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(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), 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), 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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)) 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) 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)) ---------------------------------------- (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, 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)))) 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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))) 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), 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, 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 ---------------------------------------- (151) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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, 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) -> 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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))) 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))) 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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)) 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, 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)) ---------------------------------------- (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, 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)), 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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, 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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), 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 ---------------------------------------- (155) 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)) ---------------------------------------- (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, 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), 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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), 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))) 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 ---------------------------------------- (157) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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, 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) -> 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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), 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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)) 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), 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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 ---------------------------------------- (159) 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)) ---------------------------------------- (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, 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, 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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, 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) -> 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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, 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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 ---------------------------------------- (161) 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)) ---------------------------------------- (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, 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, 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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, 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)) -> 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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, 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 ---------------------------------------- (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, 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)) -> 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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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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)) 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, 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 ---------------------------------------- (165) 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)) ---------------------------------------- (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, 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), 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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))) 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), 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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, 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 ---------------------------------------- (167) 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)) ---------------------------------------- (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, 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)) -> 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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 ---------------------------------------- (169) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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, 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)) 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), 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), 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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 ---------------------------------------- (171) 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)) ---------------------------------------- (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, 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)) -> 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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), 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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 ---------------------------------------- (173) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U21(tt, tt, isNat(x1)) -> c3(A__PLUS(a__isNat(x1), tt), MARK(tt)) ---------------------------------------- (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, 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), 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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, 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))), 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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)) 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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, 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 ---------------------------------------- (175) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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, 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))) 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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(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), 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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)) 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, 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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)) 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) 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)) ---------------------------------------- (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, 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, 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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, 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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, 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), 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))) 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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 ---------------------------------------- (179) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U21(tt, tt, tt) -> c3(A__PLUS(tt, tt), MARK(tt)) ---------------------------------------- (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, 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, 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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), 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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), 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 ---------------------------------------- (181) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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, 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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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)) 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))) -> 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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 ---------------------------------------- (183) 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)) ---------------------------------------- (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, 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, 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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, 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, 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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 ---------------------------------------- (185) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U21(tt, tt, s(x1)) -> c3(A__PLUS(s(mark(x1)), tt), MARK(tt)) ---------------------------------------- (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, 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))) 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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, 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)) -> 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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)) 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 ---------------------------------------- (187) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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, 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)) 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)) -> 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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 ---------------------------------------- (189) 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)) ---------------------------------------- (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, 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, 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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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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, 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)) 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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 ---------------------------------------- (191) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U21(tt, tt, 0) -> c3(A__PLUS(0, tt), MARK(tt)) ---------------------------------------- (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, 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, 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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, 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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) -> 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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), 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 ---------------------------------------- (193) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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, 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, 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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)) 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)), 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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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)) 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) 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))) ---------------------------------------- (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, 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)), 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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, 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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 ---------------------------------------- (197) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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, 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) -> 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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))) 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(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 ---------------------------------------- (199) 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))) ---------------------------------------- (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, 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))) 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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))) 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) -> 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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), 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), 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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 ---------------------------------------- (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, 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)) -> 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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))) 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)), 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))) 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 ---------------------------------------- (203) 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))) ---------------------------------------- (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, 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, 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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)) 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))) -> 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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)) -> 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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)) 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 ---------------------------------------- (205) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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, 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(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), 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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)) 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 ---------------------------------------- (207) 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))) ---------------------------------------- (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, 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), 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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), 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), 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__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 ---------------------------------------- (209) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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, 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), 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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), 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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))) 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 ---------------------------------------- (211) 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))) ---------------------------------------- (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, 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, 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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), 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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)) -> 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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, 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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 ---------------------------------------- (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, 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), 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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), 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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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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(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) -> 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))) 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 ---------------------------------------- (215) 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))) ---------------------------------------- (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(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)) -> 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(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, 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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(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 ---------------------------------------- (217) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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), 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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), 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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(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(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 ---------------------------------------- (219) 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)) ---------------------------------------- (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(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)), 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)), 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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)) 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 ---------------------------------------- (221) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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)) -> 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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), 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) -> 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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 ---------------------------------------- (223) 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)) ---------------------------------------- (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(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))) 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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), 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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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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) -> 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)) 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 ---------------------------------------- (225) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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(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)) -> 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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), 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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, 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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), 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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)), 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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(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 ---------------------------------------- (227) 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))) ---------------------------------------- (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(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)) -> 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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)) 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, 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)) 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 ---------------------------------------- (229) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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, 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)) 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), 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)) 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