KILLED proof of input_1HBtVKuvOm.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (6) CdtProblem (7) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxRelTRS (9) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CpxRelTRS (11) TypeInferenceProof [BOTH BOUNDS(ID, ID), 10 ms] (12) typed CpxTrs (13) OrderProof [LOWER BOUND(ID), 0 ms] (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 583 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 565 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 39 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 759 ms] (22) BEST (23) proven lower bound (24) LowerBoundPropagationProof [FINISHED, 0 ms] (25) BOUNDS(n^1, INF) (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 2276 ms] (28) typed CpxTrs (29) RewriteLemmaProof [LOWER BOUND(ID), 437 ms] (30) BOUNDS(1, INF) (31) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (32) CdtProblem (33) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (34) CdtProblem (35) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (36) CpxRelTRS (37) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (38) CpxTRS (39) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CpxWeightedTrs (41) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CpxTypedWeightedTrs (43) CompletionProof [UPPER BOUND(ID), 0 ms] (44) CpxTypedWeightedCompleteTrs (45) NarrowingProof [BOTH BOUNDS(ID, ID), 20 ms] (46) CpxTypedWeightedCompleteTrs (47) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (48) CpxRNTS (49) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CpxRNTS (51) CompletionProof [UPPER BOUND(ID), 0 ms] (52) CpxTypedWeightedCompleteTrs (53) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (54) CpxRNTS (55) CdtNarrowingProof [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) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtNarrowingProof [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) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 26 ms] (90) CdtProblem (91) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 14 ms] (98) CdtProblem (99) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 22 ms] (102) CdtProblem (103) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9 ms] (106) CdtProblem (107) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem (111) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 33 ms] (114) CdtProblem (115) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 10 ms] (120) CdtProblem (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 22 ms] (122) CdtProblem (123) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 12 ms] (124) CdtProblem (125) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (126) CdtProblem (127) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (128) CdtProblem (129) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtLeafRemovalProof [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) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (138) CdtProblem (139) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (140) CdtProblem (141) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 23 ms] (142) CdtProblem (143) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 4 ms] (144) CdtProblem (145) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (146) CdtProblem (147) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (148) CdtProblem (149) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 2 ms] (150) CdtProblem (151) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (152) CdtProblem (153) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (154) CdtProblem (155) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (156) CdtProblem (157) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (158) CdtProblem (159) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 11 ms] (160) CdtProblem (161) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3 ms] (162) CdtProblem (163) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (164) CdtProblem (165) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 8 ms] (166) CdtProblem (167) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (168) CdtProblem (169) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 22 ms] (170) CdtProblem (171) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (172) CdtProblem (173) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 25 ms] (174) CdtProblem (175) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (176) CdtProblem (177) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 101 ms] (178) CdtProblem (179) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (180) CdtProblem (181) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 18 ms] (182) CdtProblem (183) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (184) CdtProblem (185) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 12 ms] (186) CdtProblem (187) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (188) CdtProblem (189) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (190) CdtProblem (191) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (192) CdtProblem (193) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4 ms] (194) CdtProblem (195) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (196) CdtProblem (197) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 66 ms] (198) CdtProblem (199) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 10 ms] (200) CdtProblem (201) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 83 ms] (202) CdtProblem (203) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 48 ms] (204) CdtProblem (205) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (206) CdtProblem (207) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (208) CdtProblem (209) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 94 ms] (210) CdtProblem (211) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (212) CdtProblem (213) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (214) CdtProblem (215) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 62 ms] (216) CdtProblem (217) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (218) CdtProblem (219) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 27 ms] (220) CdtProblem (221) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 38 ms] (222) CdtProblem (223) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (224) CdtProblem (225) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (226) CdtProblem (227) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 42 ms] (228) CdtProblem (229) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (230) CdtProblem (231) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (232) CdtProblem (233) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 22.3 s] (234) CdtProblem (235) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (236) CdtProblem (237) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (238) CpxWeightedTrs (239) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (240) CpxTypedWeightedTrs (241) CompletionProof [UPPER BOUND(ID), 4 ms] (242) CpxTypedWeightedCompleteTrs (243) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (244) CpxRNTS (245) CompletionProof [UPPER BOUND(ID), 1 ms] (246) CpxTypedWeightedCompleteTrs (247) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (248) CpxTypedWeightedCompleteTrs (249) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (250) CpxRNTS (251) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (252) CpxRNTS ---------------------------------------- (0) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__and(tt, X) -> mark(X) a__plus(N, 0) -> mark(N) a__plus(N, s(M)) -> s(a__plus(mark(N), mark(M))) mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) mark(tt) -> tt mark(0) -> 0 mark(s(X)) -> s(mark(X)) a__and(X1, X2) -> and(X1, X2) a__plus(X1, X2) -> plus(X1, X2) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__and(tt, X) -> mark(X) a__plus(N, 0') -> mark(N) a__plus(N, s(M)) -> s(a__plus(mark(N), mark(M))) mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) mark(tt) -> tt mark(0') -> 0' mark(s(X)) -> s(mark(X)) a__and(X1, X2) -> and(X1, X2) a__plus(X1, X2) -> plus(X1, X2) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (3) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (4) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__and(tt, X) -> mark(X) a__plus(N, 0) -> mark(N) a__plus(N, s(M)) -> s(a__plus(mark(N), mark(M))) mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) mark(tt) -> tt mark(0) -> 0 mark(s(X)) -> s(mark(X)) a__and(X1, X2) -> and(X1, X2) a__plus(X1, X2) -> plus(X1, X2) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (5) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (6) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__AND(z0, z1) -> c1 A__PLUS(z0, 0) -> c2(MARK(z0)) A__PLUS(z0, s(z1)) -> c3(A__PLUS(mark(z0), mark(z1)), MARK(z0)) A__PLUS(z0, s(z1)) -> c4(A__PLUS(mark(z0), mark(z1)), MARK(z1)) A__PLUS(z0, z1) -> c5 MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c9 MARK(0) -> c10 MARK(s(z0)) -> c11(MARK(z0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__AND(z0, z1) -> c1 A__PLUS(z0, 0) -> c2(MARK(z0)) A__PLUS(z0, s(z1)) -> c3(A__PLUS(mark(z0), mark(z1)), MARK(z0)) A__PLUS(z0, s(z1)) -> c4(A__PLUS(mark(z0), mark(z1)), MARK(z1)) A__PLUS(z0, z1) -> c5 MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c9 MARK(0) -> c10 MARK(s(z0)) -> c11(MARK(z0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c1, c2_1, c3_2, c4_2, c5, c6_2, c7_2, c8_2, c9, c10, c11_1 ---------------------------------------- (7) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (8) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: A__AND(tt, z0) -> c(MARK(z0)) A__AND(z0, z1) -> c1 A__PLUS(z0, 0) -> c2(MARK(z0)) A__PLUS(z0, s(z1)) -> c3(A__PLUS(mark(z0), mark(z1)), MARK(z0)) A__PLUS(z0, s(z1)) -> c4(A__PLUS(mark(z0), mark(z1)), MARK(z1)) A__PLUS(z0, z1) -> c5 MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c9 MARK(0) -> c10 MARK(s(z0)) -> c11(MARK(z0)) The (relative) TRS S consists of the following rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Rewrite Strategy: INNERMOST ---------------------------------------- (9) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (10) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: A__AND(tt, z0) -> c(MARK(z0)) A__AND(z0, z1) -> c1 A__PLUS(z0, 0') -> c2(MARK(z0)) A__PLUS(z0, s(z1)) -> c3(A__PLUS(mark(z0), mark(z1)), MARK(z0)) A__PLUS(z0, s(z1)) -> c4(A__PLUS(mark(z0), mark(z1)), MARK(z1)) A__PLUS(z0, z1) -> c5 MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c9 MARK(0') -> c10 MARK(s(z0)) -> c11(MARK(z0)) The (relative) TRS S consists of the following rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0') -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0') -> 0' mark(s(z0)) -> s(mark(z0)) Rewrite Strategy: INNERMOST ---------------------------------------- (11) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Inferred types. ---------------------------------------- (12) Obligation: Innermost TRS: Rules: A__AND(tt, z0) -> c(MARK(z0)) A__AND(z0, z1) -> c1 A__PLUS(z0, 0') -> c2(MARK(z0)) A__PLUS(z0, s(z1)) -> c3(A__PLUS(mark(z0), mark(z1)), MARK(z0)) A__PLUS(z0, s(z1)) -> c4(A__PLUS(mark(z0), mark(z1)), MARK(z1)) A__PLUS(z0, z1) -> c5 MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c9 MARK(0') -> c10 MARK(s(z0)) -> c11(MARK(z0)) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0') -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0') -> 0' mark(s(z0)) -> s(mark(z0)) Types: A__AND :: tt:0':s:and:plus -> tt:0':s:and:plus -> c:c1 tt :: tt:0':s:and:plus c :: c6:c7:c8:c9:c10:c11 -> c:c1 MARK :: tt:0':s:and:plus -> c6:c7:c8:c9:c10:c11 c1 :: c:c1 A__PLUS :: tt:0':s:and:plus -> tt:0':s:and:plus -> c2:c3:c4:c5 0' :: tt:0':s:and:plus c2 :: c6:c7:c8:c9:c10:c11 -> c2:c3:c4:c5 s :: tt:0':s:and:plus -> tt:0':s:and:plus c3 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c2:c3:c4:c5 mark :: tt:0':s:and:plus -> tt:0':s:and:plus c4 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c2:c3:c4:c5 c5 :: c2:c3:c4:c5 and :: tt:0':s:and:plus -> tt:0':s:and:plus -> tt:0':s:and:plus c6 :: c:c1 -> c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11 plus :: tt:0':s:and:plus -> tt:0':s:and:plus -> tt:0':s:and:plus c7 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11 c8 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11 c9 :: c6:c7:c8:c9:c10:c11 c10 :: c6:c7:c8:c9:c10:c11 c11 :: c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11 a__and :: tt:0':s:and:plus -> tt:0':s:and:plus -> tt:0':s:and:plus a__plus :: tt:0':s:and:plus -> tt:0':s:and:plus -> tt:0':s:and:plus hole_c:c11_12 :: c:c1 hole_tt:0':s:and:plus2_12 :: tt:0':s:and:plus hole_c6:c7:c8:c9:c10:c113_12 :: c6:c7:c8:c9:c10:c11 hole_c2:c3:c4:c54_12 :: c2:c3:c4:c5 gen_tt:0':s:and:plus5_12 :: Nat -> tt:0':s:and:plus gen_c6:c7:c8:c9:c10:c116_12 :: Nat -> c6:c7:c8:c9:c10:c11 gen_c2:c3:c4:c57_12 :: Nat -> c2:c3:c4:c5 ---------------------------------------- (13) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: MARK, A__PLUS, mark, a__plus They will be analysed ascendingly in the following order: MARK = A__PLUS mark < MARK mark < A__PLUS mark = a__plus ---------------------------------------- (14) Obligation: Innermost TRS: Rules: A__AND(tt, z0) -> c(MARK(z0)) A__AND(z0, z1) -> c1 A__PLUS(z0, 0') -> c2(MARK(z0)) A__PLUS(z0, s(z1)) -> c3(A__PLUS(mark(z0), mark(z1)), MARK(z0)) A__PLUS(z0, s(z1)) -> c4(A__PLUS(mark(z0), mark(z1)), MARK(z1)) A__PLUS(z0, z1) -> c5 MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c9 MARK(0') -> c10 MARK(s(z0)) -> c11(MARK(z0)) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0') -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0') -> 0' mark(s(z0)) -> s(mark(z0)) Types: A__AND :: tt:0':s:and:plus -> tt:0':s:and:plus -> c:c1 tt :: tt:0':s:and:plus c :: c6:c7:c8:c9:c10:c11 -> c:c1 MARK :: tt:0':s:and:plus -> c6:c7:c8:c9:c10:c11 c1 :: c:c1 A__PLUS :: tt:0':s:and:plus -> tt:0':s:and:plus -> c2:c3:c4:c5 0' :: tt:0':s:and:plus c2 :: c6:c7:c8:c9:c10:c11 -> c2:c3:c4:c5 s :: tt:0':s:and:plus -> tt:0':s:and:plus c3 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c2:c3:c4:c5 mark :: tt:0':s:and:plus -> tt:0':s:and:plus c4 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c2:c3:c4:c5 c5 :: c2:c3:c4:c5 and :: tt:0':s:and:plus -> tt:0':s:and:plus -> tt:0':s:and:plus c6 :: c:c1 -> c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11 plus :: tt:0':s:and:plus -> tt:0':s:and:plus -> tt:0':s:and:plus c7 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11 c8 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11 c9 :: c6:c7:c8:c9:c10:c11 c10 :: c6:c7:c8:c9:c10:c11 c11 :: c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11 a__and :: tt:0':s:and:plus -> tt:0':s:and:plus -> tt:0':s:and:plus a__plus :: tt:0':s:and:plus -> tt:0':s:and:plus -> tt:0':s:and:plus hole_c:c11_12 :: c:c1 hole_tt:0':s:and:plus2_12 :: tt:0':s:and:plus hole_c6:c7:c8:c9:c10:c113_12 :: c6:c7:c8:c9:c10:c11 hole_c2:c3:c4:c54_12 :: c2:c3:c4:c5 gen_tt:0':s:and:plus5_12 :: Nat -> tt:0':s:and:plus gen_c6:c7:c8:c9:c10:c116_12 :: Nat -> c6:c7:c8:c9:c10:c11 gen_c2:c3:c4:c57_12 :: Nat -> c2:c3:c4:c5 Generator Equations: gen_tt:0':s:and:plus5_12(0) <=> tt gen_tt:0':s:and:plus5_12(+(x, 1)) <=> s(gen_tt:0':s:and:plus5_12(x)) gen_c6:c7:c8:c9:c10:c116_12(0) <=> c9 gen_c6:c7:c8:c9:c10:c116_12(+(x, 1)) <=> c6(c(c9), gen_c6:c7:c8:c9:c10:c116_12(x)) gen_c2:c3:c4:c57_12(0) <=> c2(c9) gen_c2:c3:c4:c57_12(+(x, 1)) <=> c3(gen_c2:c3:c4:c57_12(x), c9) The following defined symbols remain to be analysed: a__plus, MARK, A__PLUS, mark They will be analysed ascendingly in the following order: MARK = A__PLUS mark < MARK mark < A__PLUS mark = a__plus ---------------------------------------- (15) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: mark(gen_tt:0':s:and:plus5_12(n5861_12)) -> gen_tt:0':s:and:plus5_12(n5861_12), rt in Omega(0) Induction Base: mark(gen_tt:0':s:and:plus5_12(0)) ->_R^Omega(0) tt Induction Step: mark(gen_tt:0':s:and:plus5_12(+(n5861_12, 1))) ->_R^Omega(0) s(mark(gen_tt:0':s:and:plus5_12(n5861_12))) ->_IH s(gen_tt:0':s:and:plus5_12(c5862_12)) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (16) Obligation: Innermost TRS: Rules: A__AND(tt, z0) -> c(MARK(z0)) A__AND(z0, z1) -> c1 A__PLUS(z0, 0') -> c2(MARK(z0)) A__PLUS(z0, s(z1)) -> c3(A__PLUS(mark(z0), mark(z1)), MARK(z0)) A__PLUS(z0, s(z1)) -> c4(A__PLUS(mark(z0), mark(z1)), MARK(z1)) A__PLUS(z0, z1) -> c5 MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c9 MARK(0') -> c10 MARK(s(z0)) -> c11(MARK(z0)) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0') -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0') -> 0' mark(s(z0)) -> s(mark(z0)) Types: A__AND :: tt:0':s:and:plus -> tt:0':s:and:plus -> c:c1 tt :: tt:0':s:and:plus c :: c6:c7:c8:c9:c10:c11 -> c:c1 MARK :: tt:0':s:and:plus -> c6:c7:c8:c9:c10:c11 c1 :: c:c1 A__PLUS :: tt:0':s:and:plus -> tt:0':s:and:plus -> c2:c3:c4:c5 0' :: tt:0':s:and:plus c2 :: c6:c7:c8:c9:c10:c11 -> c2:c3:c4:c5 s :: tt:0':s:and:plus -> tt:0':s:and:plus c3 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c2:c3:c4:c5 mark :: tt:0':s:and:plus -> tt:0':s:and:plus c4 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c2:c3:c4:c5 c5 :: c2:c3:c4:c5 and :: tt:0':s:and:plus -> tt:0':s:and:plus -> tt:0':s:and:plus c6 :: c:c1 -> c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11 plus :: tt:0':s:and:plus -> tt:0':s:and:plus -> tt:0':s:and:plus c7 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11 c8 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11 c9 :: c6:c7:c8:c9:c10:c11 c10 :: c6:c7:c8:c9:c10:c11 c11 :: c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11 a__and :: tt:0':s:and:plus -> tt:0':s:and:plus -> tt:0':s:and:plus a__plus :: tt:0':s:and:plus -> tt:0':s:and:plus -> tt:0':s:and:plus hole_c:c11_12 :: c:c1 hole_tt:0':s:and:plus2_12 :: tt:0':s:and:plus hole_c6:c7:c8:c9:c10:c113_12 :: c6:c7:c8:c9:c10:c11 hole_c2:c3:c4:c54_12 :: c2:c3:c4:c5 gen_tt:0':s:and:plus5_12 :: Nat -> tt:0':s:and:plus gen_c6:c7:c8:c9:c10:c116_12 :: Nat -> c6:c7:c8:c9:c10:c11 gen_c2:c3:c4:c57_12 :: Nat -> c2:c3:c4:c5 Lemmas: mark(gen_tt:0':s:and:plus5_12(n5861_12)) -> gen_tt:0':s:and:plus5_12(n5861_12), rt in Omega(0) Generator Equations: gen_tt:0':s:and:plus5_12(0) <=> tt gen_tt:0':s:and:plus5_12(+(x, 1)) <=> s(gen_tt:0':s:and:plus5_12(x)) gen_c6:c7:c8:c9:c10:c116_12(0) <=> c9 gen_c6:c7:c8:c9:c10:c116_12(+(x, 1)) <=> c6(c(c9), gen_c6:c7:c8:c9:c10:c116_12(x)) gen_c2:c3:c4:c57_12(0) <=> c2(c9) gen_c2:c3:c4:c57_12(+(x, 1)) <=> c3(gen_c2:c3:c4:c57_12(x), c9) The following defined symbols remain to be analysed: a__plus, MARK, A__PLUS They will be analysed ascendingly in the following order: MARK = A__PLUS mark < MARK mark < A__PLUS mark = a__plus ---------------------------------------- (17) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: a__plus(gen_tt:0':s:and:plus5_12(a), gen_tt:0':s:and:plus5_12(+(1, n6520_12))) -> *8_12, rt in Omega(0) Induction Base: a__plus(gen_tt:0':s:and:plus5_12(a), gen_tt:0':s:and:plus5_12(+(1, 0))) Induction Step: a__plus(gen_tt:0':s:and:plus5_12(a), gen_tt:0':s:and:plus5_12(+(1, +(n6520_12, 1)))) ->_R^Omega(0) s(a__plus(mark(gen_tt:0':s:and:plus5_12(a)), mark(gen_tt:0':s:and:plus5_12(+(1, n6520_12))))) ->_L^Omega(0) s(a__plus(gen_tt:0':s:and:plus5_12(a), mark(gen_tt:0':s:and:plus5_12(+(1, n6520_12))))) ->_L^Omega(0) s(a__plus(gen_tt:0':s:and:plus5_12(a), gen_tt:0':s:and:plus5_12(+(1, n6520_12)))) ->_IH s(*8_12) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (18) Obligation: Innermost TRS: Rules: A__AND(tt, z0) -> c(MARK(z0)) A__AND(z0, z1) -> c1 A__PLUS(z0, 0') -> c2(MARK(z0)) A__PLUS(z0, s(z1)) -> c3(A__PLUS(mark(z0), mark(z1)), MARK(z0)) A__PLUS(z0, s(z1)) -> c4(A__PLUS(mark(z0), mark(z1)), MARK(z1)) A__PLUS(z0, z1) -> c5 MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c9 MARK(0') -> c10 MARK(s(z0)) -> c11(MARK(z0)) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0') -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0') -> 0' mark(s(z0)) -> s(mark(z0)) Types: A__AND :: tt:0':s:and:plus -> tt:0':s:and:plus -> c:c1 tt :: tt:0':s:and:plus c :: c6:c7:c8:c9:c10:c11 -> c:c1 MARK :: tt:0':s:and:plus -> c6:c7:c8:c9:c10:c11 c1 :: c:c1 A__PLUS :: tt:0':s:and:plus -> tt:0':s:and:plus -> c2:c3:c4:c5 0' :: tt:0':s:and:plus c2 :: c6:c7:c8:c9:c10:c11 -> c2:c3:c4:c5 s :: tt:0':s:and:plus -> tt:0':s:and:plus c3 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c2:c3:c4:c5 mark :: tt:0':s:and:plus -> tt:0':s:and:plus c4 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c2:c3:c4:c5 c5 :: c2:c3:c4:c5 and :: tt:0':s:and:plus -> tt:0':s:and:plus -> tt:0':s:and:plus c6 :: c:c1 -> c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11 plus :: tt:0':s:and:plus -> tt:0':s:and:plus -> tt:0':s:and:plus c7 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11 c8 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11 c9 :: c6:c7:c8:c9:c10:c11 c10 :: c6:c7:c8:c9:c10:c11 c11 :: c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11 a__and :: tt:0':s:and:plus -> tt:0':s:and:plus -> tt:0':s:and:plus a__plus :: tt:0':s:and:plus -> tt:0':s:and:plus -> tt:0':s:and:plus hole_c:c11_12 :: c:c1 hole_tt:0':s:and:plus2_12 :: tt:0':s:and:plus hole_c6:c7:c8:c9:c10:c113_12 :: c6:c7:c8:c9:c10:c11 hole_c2:c3:c4:c54_12 :: c2:c3:c4:c5 gen_tt:0':s:and:plus5_12 :: Nat -> tt:0':s:and:plus gen_c6:c7:c8:c9:c10:c116_12 :: Nat -> c6:c7:c8:c9:c10:c11 gen_c2:c3:c4:c57_12 :: Nat -> c2:c3:c4:c5 Lemmas: mark(gen_tt:0':s:and:plus5_12(n5861_12)) -> gen_tt:0':s:and:plus5_12(n5861_12), rt in Omega(0) a__plus(gen_tt:0':s:and:plus5_12(a), gen_tt:0':s:and:plus5_12(+(1, n6520_12))) -> *8_12, rt in Omega(0) Generator Equations: gen_tt:0':s:and:plus5_12(0) <=> tt gen_tt:0':s:and:plus5_12(+(x, 1)) <=> s(gen_tt:0':s:and:plus5_12(x)) gen_c6:c7:c8:c9:c10:c116_12(0) <=> c9 gen_c6:c7:c8:c9:c10:c116_12(+(x, 1)) <=> c6(c(c9), gen_c6:c7:c8:c9:c10:c116_12(x)) gen_c2:c3:c4:c57_12(0) <=> c2(c9) gen_c2:c3:c4:c57_12(+(x, 1)) <=> c3(gen_c2:c3:c4:c57_12(x), c9) The following defined symbols remain to be analysed: mark, MARK, A__PLUS They will be analysed ascendingly in the following order: MARK = A__PLUS mark < MARK mark < A__PLUS mark = a__plus ---------------------------------------- (19) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: mark(gen_tt:0':s:and:plus5_12(n8897_12)) -> gen_tt:0':s:and:plus5_12(n8897_12), rt in Omega(0) Induction Base: mark(gen_tt:0':s:and:plus5_12(0)) ->_R^Omega(0) tt Induction Step: mark(gen_tt:0':s:and:plus5_12(+(n8897_12, 1))) ->_R^Omega(0) s(mark(gen_tt:0':s:and:plus5_12(n8897_12))) ->_IH s(gen_tt:0':s:and:plus5_12(c8898_12)) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (20) Obligation: Innermost TRS: Rules: A__AND(tt, z0) -> c(MARK(z0)) A__AND(z0, z1) -> c1 A__PLUS(z0, 0') -> c2(MARK(z0)) A__PLUS(z0, s(z1)) -> c3(A__PLUS(mark(z0), mark(z1)), MARK(z0)) A__PLUS(z0, s(z1)) -> c4(A__PLUS(mark(z0), mark(z1)), MARK(z1)) A__PLUS(z0, z1) -> c5 MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c9 MARK(0') -> c10 MARK(s(z0)) -> c11(MARK(z0)) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0') -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0') -> 0' mark(s(z0)) -> s(mark(z0)) Types: A__AND :: tt:0':s:and:plus -> tt:0':s:and:plus -> c:c1 tt :: tt:0':s:and:plus c :: c6:c7:c8:c9:c10:c11 -> c:c1 MARK :: tt:0':s:and:plus -> c6:c7:c8:c9:c10:c11 c1 :: c:c1 A__PLUS :: tt:0':s:and:plus -> tt:0':s:and:plus -> c2:c3:c4:c5 0' :: tt:0':s:and:plus c2 :: c6:c7:c8:c9:c10:c11 -> c2:c3:c4:c5 s :: tt:0':s:and:plus -> tt:0':s:and:plus c3 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c2:c3:c4:c5 mark :: tt:0':s:and:plus -> tt:0':s:and:plus c4 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c2:c3:c4:c5 c5 :: c2:c3:c4:c5 and :: tt:0':s:and:plus -> tt:0':s:and:plus -> tt:0':s:and:plus c6 :: c:c1 -> c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11 plus :: tt:0':s:and:plus -> tt:0':s:and:plus -> tt:0':s:and:plus c7 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11 c8 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11 c9 :: c6:c7:c8:c9:c10:c11 c10 :: c6:c7:c8:c9:c10:c11 c11 :: c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11 a__and :: tt:0':s:and:plus -> tt:0':s:and:plus -> tt:0':s:and:plus a__plus :: tt:0':s:and:plus -> tt:0':s:and:plus -> tt:0':s:and:plus hole_c:c11_12 :: c:c1 hole_tt:0':s:and:plus2_12 :: tt:0':s:and:plus hole_c6:c7:c8:c9:c10:c113_12 :: c6:c7:c8:c9:c10:c11 hole_c2:c3:c4:c54_12 :: c2:c3:c4:c5 gen_tt:0':s:and:plus5_12 :: Nat -> tt:0':s:and:plus gen_c6:c7:c8:c9:c10:c116_12 :: Nat -> c6:c7:c8:c9:c10:c11 gen_c2:c3:c4:c57_12 :: Nat -> c2:c3:c4:c5 Lemmas: mark(gen_tt:0':s:and:plus5_12(n8897_12)) -> gen_tt:0':s:and:plus5_12(n8897_12), rt in Omega(0) a__plus(gen_tt:0':s:and:plus5_12(a), gen_tt:0':s:and:plus5_12(+(1, n6520_12))) -> *8_12, rt in Omega(0) Generator Equations: gen_tt:0':s:and:plus5_12(0) <=> tt gen_tt:0':s:and:plus5_12(+(x, 1)) <=> s(gen_tt:0':s:and:plus5_12(x)) gen_c6:c7:c8:c9:c10:c116_12(0) <=> c9 gen_c6:c7:c8:c9:c10:c116_12(+(x, 1)) <=> c6(c(c9), gen_c6:c7:c8:c9:c10:c116_12(x)) gen_c2:c3:c4:c57_12(0) <=> c2(c9) gen_c2:c3:c4:c57_12(+(x, 1)) <=> c3(gen_c2:c3:c4:c57_12(x), c9) The following defined symbols remain to be analysed: A__PLUS, MARK They will be analysed ascendingly in the following order: MARK = A__PLUS ---------------------------------------- (21) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: A__PLUS(gen_tt:0':s:and:plus5_12(a), gen_tt:0':s:and:plus5_12(+(1, n9659_12))) -> *8_12, rt in Omega(n9659_12) Induction Base: A__PLUS(gen_tt:0':s:and:plus5_12(a), gen_tt:0':s:and:plus5_12(+(1, 0))) Induction Step: A__PLUS(gen_tt:0':s:and:plus5_12(a), gen_tt:0':s:and:plus5_12(+(1, +(n9659_12, 1)))) ->_R^Omega(1) c3(A__PLUS(mark(gen_tt:0':s:and:plus5_12(a)), mark(gen_tt:0':s:and:plus5_12(+(1, n9659_12)))), MARK(gen_tt:0':s:and:plus5_12(a))) ->_L^Omega(0) c3(A__PLUS(gen_tt:0':s:and:plus5_12(a), mark(gen_tt:0':s:and:plus5_12(+(1, n9659_12)))), MARK(gen_tt:0':s:and:plus5_12(a))) ->_L^Omega(0) c3(A__PLUS(gen_tt:0':s:and:plus5_12(a), gen_tt:0':s:and:plus5_12(+(1, n9659_12))), MARK(gen_tt:0':s:and:plus5_12(a))) ->_IH c3(*8_12, MARK(gen_tt:0':s:and:plus5_12(a))) We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (22) Complex Obligation (BEST) ---------------------------------------- (23) Obligation: Proved the lower bound n^1 for the following obligation: Innermost TRS: Rules: A__AND(tt, z0) -> c(MARK(z0)) A__AND(z0, z1) -> c1 A__PLUS(z0, 0') -> c2(MARK(z0)) A__PLUS(z0, s(z1)) -> c3(A__PLUS(mark(z0), mark(z1)), MARK(z0)) A__PLUS(z0, s(z1)) -> c4(A__PLUS(mark(z0), mark(z1)), MARK(z1)) A__PLUS(z0, z1) -> c5 MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c9 MARK(0') -> c10 MARK(s(z0)) -> c11(MARK(z0)) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0') -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0') -> 0' mark(s(z0)) -> s(mark(z0)) Types: A__AND :: tt:0':s:and:plus -> tt:0':s:and:plus -> c:c1 tt :: tt:0':s:and:plus c :: c6:c7:c8:c9:c10:c11 -> c:c1 MARK :: tt:0':s:and:plus -> c6:c7:c8:c9:c10:c11 c1 :: c:c1 A__PLUS :: tt:0':s:and:plus -> tt:0':s:and:plus -> c2:c3:c4:c5 0' :: tt:0':s:and:plus c2 :: c6:c7:c8:c9:c10:c11 -> c2:c3:c4:c5 s :: tt:0':s:and:plus -> tt:0':s:and:plus c3 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c2:c3:c4:c5 mark :: tt:0':s:and:plus -> tt:0':s:and:plus c4 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c2:c3:c4:c5 c5 :: c2:c3:c4:c5 and :: tt:0':s:and:plus -> tt:0':s:and:plus -> tt:0':s:and:plus c6 :: c:c1 -> c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11 plus :: tt:0':s:and:plus -> tt:0':s:and:plus -> tt:0':s:and:plus c7 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11 c8 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11 c9 :: c6:c7:c8:c9:c10:c11 c10 :: c6:c7:c8:c9:c10:c11 c11 :: c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11 a__and :: tt:0':s:and:plus -> tt:0':s:and:plus -> tt:0':s:and:plus a__plus :: tt:0':s:and:plus -> tt:0':s:and:plus -> tt:0':s:and:plus hole_c:c11_12 :: c:c1 hole_tt:0':s:and:plus2_12 :: tt:0':s:and:plus hole_c6:c7:c8:c9:c10:c113_12 :: c6:c7:c8:c9:c10:c11 hole_c2:c3:c4:c54_12 :: c2:c3:c4:c5 gen_tt:0':s:and:plus5_12 :: Nat -> tt:0':s:and:plus gen_c6:c7:c8:c9:c10:c116_12 :: Nat -> c6:c7:c8:c9:c10:c11 gen_c2:c3:c4:c57_12 :: Nat -> c2:c3:c4:c5 Lemmas: mark(gen_tt:0':s:and:plus5_12(n8897_12)) -> gen_tt:0':s:and:plus5_12(n8897_12), rt in Omega(0) a__plus(gen_tt:0':s:and:plus5_12(a), gen_tt:0':s:and:plus5_12(+(1, n6520_12))) -> *8_12, rt in Omega(0) Generator Equations: gen_tt:0':s:and:plus5_12(0) <=> tt gen_tt:0':s:and:plus5_12(+(x, 1)) <=> s(gen_tt:0':s:and:plus5_12(x)) gen_c6:c7:c8:c9:c10:c116_12(0) <=> c9 gen_c6:c7:c8:c9:c10:c116_12(+(x, 1)) <=> c6(c(c9), gen_c6:c7:c8:c9:c10:c116_12(x)) gen_c2:c3:c4:c57_12(0) <=> c2(c9) gen_c2:c3:c4:c57_12(+(x, 1)) <=> c3(gen_c2:c3:c4:c57_12(x), c9) The following defined symbols remain to be analysed: A__PLUS, MARK They will be analysed ascendingly in the following order: MARK = A__PLUS ---------------------------------------- (24) LowerBoundPropagationProof (FINISHED) Propagated lower bound. ---------------------------------------- (25) BOUNDS(n^1, INF) ---------------------------------------- (26) Obligation: Innermost TRS: Rules: A__AND(tt, z0) -> c(MARK(z0)) A__AND(z0, z1) -> c1 A__PLUS(z0, 0') -> c2(MARK(z0)) A__PLUS(z0, s(z1)) -> c3(A__PLUS(mark(z0), mark(z1)), MARK(z0)) A__PLUS(z0, s(z1)) -> c4(A__PLUS(mark(z0), mark(z1)), MARK(z1)) A__PLUS(z0, z1) -> c5 MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c9 MARK(0') -> c10 MARK(s(z0)) -> c11(MARK(z0)) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0') -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0') -> 0' mark(s(z0)) -> s(mark(z0)) Types: A__AND :: tt:0':s:and:plus -> tt:0':s:and:plus -> c:c1 tt :: tt:0':s:and:plus c :: c6:c7:c8:c9:c10:c11 -> c:c1 MARK :: tt:0':s:and:plus -> c6:c7:c8:c9:c10:c11 c1 :: c:c1 A__PLUS :: tt:0':s:and:plus -> tt:0':s:and:plus -> c2:c3:c4:c5 0' :: tt:0':s:and:plus c2 :: c6:c7:c8:c9:c10:c11 -> c2:c3:c4:c5 s :: tt:0':s:and:plus -> tt:0':s:and:plus c3 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c2:c3:c4:c5 mark :: tt:0':s:and:plus -> tt:0':s:and:plus c4 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c2:c3:c4:c5 c5 :: c2:c3:c4:c5 and :: tt:0':s:and:plus -> tt:0':s:and:plus -> tt:0':s:and:plus c6 :: c:c1 -> c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11 plus :: tt:0':s:and:plus -> tt:0':s:and:plus -> tt:0':s:and:plus c7 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11 c8 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11 c9 :: c6:c7:c8:c9:c10:c11 c10 :: c6:c7:c8:c9:c10:c11 c11 :: c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11 a__and :: tt:0':s:and:plus -> tt:0':s:and:plus -> tt:0':s:and:plus a__plus :: tt:0':s:and:plus -> tt:0':s:and:plus -> tt:0':s:and:plus hole_c:c11_12 :: c:c1 hole_tt:0':s:and:plus2_12 :: tt:0':s:and:plus hole_c6:c7:c8:c9:c10:c113_12 :: c6:c7:c8:c9:c10:c11 hole_c2:c3:c4:c54_12 :: c2:c3:c4:c5 gen_tt:0':s:and:plus5_12 :: Nat -> tt:0':s:and:plus gen_c6:c7:c8:c9:c10:c116_12 :: Nat -> c6:c7:c8:c9:c10:c11 gen_c2:c3:c4:c57_12 :: Nat -> c2:c3:c4:c5 Lemmas: mark(gen_tt:0':s:and:plus5_12(n8897_12)) -> gen_tt:0':s:and:plus5_12(n8897_12), rt in Omega(0) a__plus(gen_tt:0':s:and:plus5_12(a), gen_tt:0':s:and:plus5_12(+(1, n6520_12))) -> *8_12, rt in Omega(0) A__PLUS(gen_tt:0':s:and:plus5_12(a), gen_tt:0':s:and:plus5_12(+(1, n9659_12))) -> *8_12, rt in Omega(n9659_12) Generator Equations: gen_tt:0':s:and:plus5_12(0) <=> tt gen_tt:0':s:and:plus5_12(+(x, 1)) <=> s(gen_tt:0':s:and:plus5_12(x)) gen_c6:c7:c8:c9:c10:c116_12(0) <=> c9 gen_c6:c7:c8:c9:c10:c116_12(+(x, 1)) <=> c6(c(c9), gen_c6:c7:c8:c9:c10:c116_12(x)) gen_c2:c3:c4:c57_12(0) <=> c2(c9) gen_c2:c3:c4:c57_12(+(x, 1)) <=> c3(gen_c2:c3:c4:c57_12(x), c9) The following defined symbols remain to be analysed: MARK They will be analysed ascendingly in the following order: MARK = A__PLUS ---------------------------------------- (27) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: MARK(gen_tt:0':s:and:plus5_12(+(1, n16024_12))) -> *8_12, rt in Omega(n16024_12) Induction Base: MARK(gen_tt:0':s:and:plus5_12(+(1, 0))) Induction Step: MARK(gen_tt:0':s:and:plus5_12(+(1, +(n16024_12, 1)))) ->_R^Omega(1) c11(MARK(gen_tt:0':s:and:plus5_12(+(1, n16024_12)))) ->_IH c11(*8_12) We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (28) Obligation: Innermost TRS: Rules: A__AND(tt, z0) -> c(MARK(z0)) A__AND(z0, z1) -> c1 A__PLUS(z0, 0') -> c2(MARK(z0)) A__PLUS(z0, s(z1)) -> c3(A__PLUS(mark(z0), mark(z1)), MARK(z0)) A__PLUS(z0, s(z1)) -> c4(A__PLUS(mark(z0), mark(z1)), MARK(z1)) A__PLUS(z0, z1) -> c5 MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c9 MARK(0') -> c10 MARK(s(z0)) -> c11(MARK(z0)) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0') -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0') -> 0' mark(s(z0)) -> s(mark(z0)) Types: A__AND :: tt:0':s:and:plus -> tt:0':s:and:plus -> c:c1 tt :: tt:0':s:and:plus c :: c6:c7:c8:c9:c10:c11 -> c:c1 MARK :: tt:0':s:and:plus -> c6:c7:c8:c9:c10:c11 c1 :: c:c1 A__PLUS :: tt:0':s:and:plus -> tt:0':s:and:plus -> c2:c3:c4:c5 0' :: tt:0':s:and:plus c2 :: c6:c7:c8:c9:c10:c11 -> c2:c3:c4:c5 s :: tt:0':s:and:plus -> tt:0':s:and:plus c3 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c2:c3:c4:c5 mark :: tt:0':s:and:plus -> tt:0':s:and:plus c4 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c2:c3:c4:c5 c5 :: c2:c3:c4:c5 and :: tt:0':s:and:plus -> tt:0':s:and:plus -> tt:0':s:and:plus c6 :: c:c1 -> c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11 plus :: tt:0':s:and:plus -> tt:0':s:and:plus -> tt:0':s:and:plus c7 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11 c8 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11 c9 :: c6:c7:c8:c9:c10:c11 c10 :: c6:c7:c8:c9:c10:c11 c11 :: c6:c7:c8:c9:c10:c11 -> c6:c7:c8:c9:c10:c11 a__and :: tt:0':s:and:plus -> tt:0':s:and:plus -> tt:0':s:and:plus a__plus :: tt:0':s:and:plus -> tt:0':s:and:plus -> tt:0':s:and:plus hole_c:c11_12 :: c:c1 hole_tt:0':s:and:plus2_12 :: tt:0':s:and:plus hole_c6:c7:c8:c9:c10:c113_12 :: c6:c7:c8:c9:c10:c11 hole_c2:c3:c4:c54_12 :: c2:c3:c4:c5 gen_tt:0':s:and:plus5_12 :: Nat -> tt:0':s:and:plus gen_c6:c7:c8:c9:c10:c116_12 :: Nat -> c6:c7:c8:c9:c10:c11 gen_c2:c3:c4:c57_12 :: Nat -> c2:c3:c4:c5 Lemmas: mark(gen_tt:0':s:and:plus5_12(n8897_12)) -> gen_tt:0':s:and:plus5_12(n8897_12), rt in Omega(0) a__plus(gen_tt:0':s:and:plus5_12(a), gen_tt:0':s:and:plus5_12(+(1, n6520_12))) -> *8_12, rt in Omega(0) A__PLUS(gen_tt:0':s:and:plus5_12(a), gen_tt:0':s:and:plus5_12(+(1, n9659_12))) -> *8_12, rt in Omega(n9659_12) MARK(gen_tt:0':s:and:plus5_12(+(1, n16024_12))) -> *8_12, rt in Omega(n16024_12) Generator Equations: gen_tt:0':s:and:plus5_12(0) <=> tt gen_tt:0':s:and:plus5_12(+(x, 1)) <=> s(gen_tt:0':s:and:plus5_12(x)) gen_c6:c7:c8:c9:c10:c116_12(0) <=> c9 gen_c6:c7:c8:c9:c10:c116_12(+(x, 1)) <=> c6(c(c9), gen_c6:c7:c8:c9:c10:c116_12(x)) gen_c2:c3:c4:c57_12(0) <=> c2(c9) gen_c2:c3:c4:c57_12(+(x, 1)) <=> c3(gen_c2:c3:c4:c57_12(x), c9) The following defined symbols remain to be analysed: A__PLUS They will be analysed ascendingly in the following order: MARK = A__PLUS ---------------------------------------- (29) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: A__PLUS(gen_tt:0':s:and:plus5_12(a), gen_tt:0':s:and:plus5_12(+(1, n26472_12))) -> *8_12, rt in Omega(n26472_12) Induction Base: A__PLUS(gen_tt:0':s:and:plus5_12(a), gen_tt:0':s:and:plus5_12(+(1, 0))) Induction Step: A__PLUS(gen_tt:0':s:and:plus5_12(a), gen_tt:0':s:and:plus5_12(+(1, +(n26472_12, 1)))) ->_R^Omega(1) c3(A__PLUS(mark(gen_tt:0':s:and:plus5_12(a)), mark(gen_tt:0':s:and:plus5_12(+(1, n26472_12)))), MARK(gen_tt:0':s:and:plus5_12(a))) ->_L^Omega(0) c3(A__PLUS(gen_tt:0':s:and:plus5_12(a), mark(gen_tt:0':s:and:plus5_12(+(1, n26472_12)))), MARK(gen_tt:0':s:and:plus5_12(a))) ->_L^Omega(0) c3(A__PLUS(gen_tt:0':s:and:plus5_12(a), gen_tt:0':s:and:plus5_12(+(1, n26472_12))), MARK(gen_tt:0':s:and:plus5_12(a))) ->_IH c3(*8_12, MARK(gen_tt:0':s:and:plus5_12(a))) We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (30) BOUNDS(1, INF) ---------------------------------------- (31) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (32) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__AND(z0, z1) -> c1 A__PLUS(z0, 0) -> c2(MARK(z0)) A__PLUS(z0, s(z1)) -> c3(A__PLUS(mark(z0), mark(z1)), MARK(z0)) A__PLUS(z0, s(z1)) -> c4(A__PLUS(mark(z0), mark(z1)), MARK(z1)) A__PLUS(z0, z1) -> c5 MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c9 MARK(0) -> c10 MARK(s(z0)) -> c11(MARK(z0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__AND(z0, z1) -> c1 A__PLUS(z0, 0) -> c2(MARK(z0)) A__PLUS(z0, s(z1)) -> c3(A__PLUS(mark(z0), mark(z1)), MARK(z0)) A__PLUS(z0, s(z1)) -> c4(A__PLUS(mark(z0), mark(z1)), MARK(z1)) A__PLUS(z0, z1) -> c5 MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c9 MARK(0) -> c10 MARK(s(z0)) -> c11(MARK(z0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c1, c2_1, c3_2, c4_2, c5, c6_2, c7_2, c8_2, c9, c10, c11_1 ---------------------------------------- (33) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing nodes: MARK(0) -> c10 A__AND(z0, z1) -> c1 MARK(tt) -> c9 A__PLUS(z0, z1) -> c5 ---------------------------------------- (34) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) A__PLUS(z0, s(z1)) -> c3(A__PLUS(mark(z0), mark(z1)), MARK(z0)) A__PLUS(z0, s(z1)) -> c4(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) A__PLUS(z0, s(z1)) -> c3(A__PLUS(mark(z0), mark(z1)), MARK(z0)) A__PLUS(z0, s(z1)) -> c4(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c3_2, c4_2, c6_2, c7_2, c8_2, c11_1 ---------------------------------------- (35) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (36) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) A__PLUS(z0, s(z1)) -> c3(A__PLUS(mark(z0), mark(z1)), MARK(z0)) A__PLUS(z0, s(z1)) -> c4(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) The (relative) TRS S consists of the following rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Rewrite Strategy: INNERMOST ---------------------------------------- (37) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (38) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) A__PLUS(z0, s(z1)) -> c3(A__PLUS(mark(z0), mark(z1)), MARK(z0)) A__PLUS(z0, s(z1)) -> c4(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (39) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (40) 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__AND(tt, z0) -> c(MARK(z0)) [1] A__PLUS(z0, 0) -> c2(MARK(z0)) [1] A__PLUS(z0, s(z1)) -> c3(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] A__PLUS(z0, s(z1)) -> c4(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) [1] MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(s(z0)) -> c11(MARK(z0)) [1] a__and(tt, z0) -> mark(z0) [0] a__and(z0, z1) -> and(z0, z1) [0] a__plus(z0, 0) -> mark(z0) [0] a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) [0] a__plus(z0, z1) -> plus(z0, z1) [0] mark(and(z0, z1)) -> a__and(mark(z0), z1) [0] mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0] mark(tt) -> tt [0] mark(0) -> 0 [0] mark(s(z0)) -> s(mark(z0)) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (41) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (42) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__AND(tt, z0) -> c(MARK(z0)) [1] A__PLUS(z0, 0) -> c2(MARK(z0)) [1] A__PLUS(z0, s(z1)) -> c3(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] A__PLUS(z0, s(z1)) -> c4(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) [1] MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(s(z0)) -> c11(MARK(z0)) [1] a__and(tt, z0) -> mark(z0) [0] a__and(z0, z1) -> and(z0, z1) [0] a__plus(z0, 0) -> mark(z0) [0] a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) [0] a__plus(z0, z1) -> plus(z0, z1) [0] mark(and(z0, z1)) -> a__and(mark(z0), z1) [0] mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0] mark(tt) -> tt [0] mark(0) -> 0 [0] mark(s(z0)) -> s(mark(z0)) [0] The TRS has the following type information: A__AND :: tt:0:s:and:plus -> tt:0:s:and:plus -> c tt :: tt:0:s:and:plus c :: c6:c7:c8:c11 -> c MARK :: tt:0:s:and:plus -> c6:c7:c8:c11 A__PLUS :: tt:0:s:and:plus -> tt:0:s:and:plus -> c2:c3:c4 0 :: tt:0:s:and:plus c2 :: c6:c7:c8:c11 -> c2:c3:c4 s :: tt:0:s:and:plus -> tt:0:s:and:plus c3 :: c2:c3:c4 -> c6:c7:c8:c11 -> c2:c3:c4 mark :: tt:0:s:and:plus -> tt:0:s:and:plus c4 :: c2:c3:c4 -> c6:c7:c8:c11 -> c2:c3:c4 and :: tt:0:s:and:plus -> tt:0:s:and:plus -> tt:0:s:and:plus c6 :: c -> c6:c7:c8:c11 -> c6:c7:c8:c11 plus :: tt:0:s:and:plus -> tt:0:s:and:plus -> tt:0:s:and:plus c7 :: c2:c3:c4 -> c6:c7:c8:c11 -> c6:c7:c8:c11 c8 :: c2:c3:c4 -> c6:c7:c8:c11 -> c6:c7:c8:c11 c11 :: c6:c7:c8:c11 -> c6:c7:c8:c11 a__and :: tt:0:s:and:plus -> tt:0:s:and:plus -> tt:0:s:and:plus a__plus :: tt:0:s:and:plus -> tt:0:s:and:plus -> tt:0:s:and:plus Rewrite Strategy: INNERMOST ---------------------------------------- (43) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: A__AND_2 A__PLUS_2 MARK_1 (c) The following functions are completely defined: a__and_2 a__plus_2 mark_1 Due to the following rules being added: a__and(v0, v1) -> null_a__and [0] a__plus(v0, v1) -> null_a__plus [0] mark(v0) -> null_mark [0] And the following fresh constants: null_a__and, null_a__plus, null_mark, const, const1, const2 ---------------------------------------- (44) 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__AND(tt, z0) -> c(MARK(z0)) [1] A__PLUS(z0, 0) -> c2(MARK(z0)) [1] A__PLUS(z0, s(z1)) -> c3(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] A__PLUS(z0, s(z1)) -> c4(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) [1] MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(s(z0)) -> c11(MARK(z0)) [1] a__and(tt, z0) -> mark(z0) [0] a__and(z0, z1) -> and(z0, z1) [0] a__plus(z0, 0) -> mark(z0) [0] a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) [0] a__plus(z0, z1) -> plus(z0, z1) [0] mark(and(z0, z1)) -> a__and(mark(z0), z1) [0] mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0] mark(tt) -> tt [0] mark(0) -> 0 [0] mark(s(z0)) -> s(mark(z0)) [0] a__and(v0, v1) -> null_a__and [0] a__plus(v0, v1) -> null_a__plus [0] mark(v0) -> null_mark [0] The TRS has the following type information: A__AND :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> c tt :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark c :: c6:c7:c8:c11 -> c MARK :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> c6:c7:c8:c11 A__PLUS :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> c2:c3:c4 0 :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark c2 :: c6:c7:c8:c11 -> c2:c3:c4 s :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> tt:0:s:and:plus:null_a__and:null_a__plus:null_mark c3 :: c2:c3:c4 -> c6:c7:c8:c11 -> c2:c3:c4 mark :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> tt:0:s:and:plus:null_a__and:null_a__plus:null_mark c4 :: c2:c3:c4 -> c6:c7:c8:c11 -> c2:c3:c4 and :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> tt:0:s:and:plus:null_a__and:null_a__plus:null_mark c6 :: c -> c6:c7:c8:c11 -> c6:c7:c8:c11 plus :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> tt:0:s:and:plus:null_a__and:null_a__plus:null_mark c7 :: c2:c3:c4 -> c6:c7:c8:c11 -> c6:c7:c8:c11 c8 :: c2:c3:c4 -> c6:c7:c8:c11 -> c6:c7:c8:c11 c11 :: c6:c7:c8:c11 -> c6:c7:c8:c11 a__and :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> tt:0:s:and:plus:null_a__and:null_a__plus:null_mark a__plus :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> tt:0:s:and:plus:null_a__and:null_a__plus:null_mark null_a__and :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark null_a__plus :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark null_mark :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark const :: c const1 :: c6:c7:c8:c11 const2 :: c2:c3:c4 Rewrite Strategy: INNERMOST ---------------------------------------- (45) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (46) 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__AND(tt, z0) -> c(MARK(z0)) [1] A__PLUS(z0, 0) -> c2(MARK(z0)) [1] A__PLUS(z0, s(z1)) -> c3(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] A__PLUS(z0, s(z1)) -> c4(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(and(and(z041, z127), z1)) -> c6(A__AND(a__and(mark(z041), z127), z1), MARK(and(z041, z127))) [1] MARK(and(plus(z042, z128), z1)) -> c6(A__AND(a__plus(mark(z042), mark(z128)), z1), MARK(plus(z042, z128))) [1] MARK(and(tt, z1)) -> c6(A__AND(tt, z1), MARK(tt)) [1] MARK(and(0, z1)) -> c6(A__AND(0, z1), MARK(0)) [1] MARK(and(s(z043), z1)) -> c6(A__AND(s(mark(z043)), z1), MARK(s(z043))) [1] MARK(and(z0, z1)) -> c6(A__AND(null_mark, z1), MARK(z0)) [1] MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(s(z0)) -> c11(MARK(z0)) [1] a__and(tt, z0) -> mark(z0) [0] a__and(z0, z1) -> and(z0, z1) [0] a__plus(z0, 0) -> mark(z0) [0] a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) [0] a__plus(z0, z1) -> plus(z0, z1) [0] mark(and(and(z0107, z171), z1)) -> a__and(a__and(mark(z0107), z171), z1) [0] mark(and(plus(z0108, z172), z1)) -> a__and(a__plus(mark(z0108), mark(z172)), z1) [0] mark(and(tt, z1)) -> a__and(tt, z1) [0] mark(and(0, z1)) -> a__and(0, z1) [0] mark(and(s(z0109), z1)) -> a__and(s(mark(z0109)), z1) [0] mark(and(z0, z1)) -> a__and(null_mark, z1) [0] mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0] mark(tt) -> tt [0] mark(0) -> 0 [0] mark(s(z0)) -> s(mark(z0)) [0] a__and(v0, v1) -> null_a__and [0] a__plus(v0, v1) -> null_a__plus [0] mark(v0) -> null_mark [0] The TRS has the following type information: A__AND :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> c tt :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark c :: c6:c7:c8:c11 -> c MARK :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> c6:c7:c8:c11 A__PLUS :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> c2:c3:c4 0 :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark c2 :: c6:c7:c8:c11 -> c2:c3:c4 s :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> tt:0:s:and:plus:null_a__and:null_a__plus:null_mark c3 :: c2:c3:c4 -> c6:c7:c8:c11 -> c2:c3:c4 mark :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> tt:0:s:and:plus:null_a__and:null_a__plus:null_mark c4 :: c2:c3:c4 -> c6:c7:c8:c11 -> c2:c3:c4 and :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> tt:0:s:and:plus:null_a__and:null_a__plus:null_mark c6 :: c -> c6:c7:c8:c11 -> c6:c7:c8:c11 plus :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> tt:0:s:and:plus:null_a__and:null_a__plus:null_mark c7 :: c2:c3:c4 -> c6:c7:c8:c11 -> c6:c7:c8:c11 c8 :: c2:c3:c4 -> c6:c7:c8:c11 -> c6:c7:c8:c11 c11 :: c6:c7:c8:c11 -> c6:c7:c8:c11 a__and :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> tt:0:s:and:plus:null_a__and:null_a__plus:null_mark a__plus :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> tt:0:s:and:plus:null_a__and:null_a__plus:null_mark null_a__and :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark null_a__plus :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark null_mark :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark const :: c const1 :: c6:c7:c8:c11 const2 :: c2:c3:c4 Rewrite Strategy: INNERMOST ---------------------------------------- (47) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: tt => 1 0 => 0 null_a__and => 0 null_a__plus => 0 null_mark => 0 const => 0 const1 => 0 const2 => 0 ---------------------------------------- (48) Obligation: Complexity RNTS consisting of the following rules: A__AND(z, z') -{ 1 }-> 1 + MARK(z0) :|: z = 1, z0 >= 0, z' = z0 A__PLUS(z, z') -{ 1 }-> 1 + MARK(z0) :|: z = z0, z0 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 A__PLUS(z, z') -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z1) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__AND(a__plus(mark(z042), mark(z128)), z1) + MARK(1 + z042 + z128) :|: z042 >= 0, z = 1 + (1 + z042 + z128) + z1, z1 >= 0, z128 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__and(mark(z041), z127), z1) + MARK(1 + z041 + z127) :|: z1 >= 0, z041 >= 0, z = 1 + (1 + z041 + z127) + z1, z127 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(1, z1) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 MARK(z) -{ 1 }-> 1 + A__AND(0, z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__AND(0, z1) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 MARK(z) -{ 1 }-> 1 + A__AND(1 + mark(z043), z1) + MARK(1 + z043) :|: z1 >= 0, z043 >= 0, z = 1 + (1 + z043) + z1 a__and(z, z') -{ 0 }-> mark(z0) :|: z = 1, z0 >= 0, z' = z0 a__and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__and(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__plus(z, z') -{ 0 }-> mark(z0) :|: z = z0, z0 >= 0, z' = 0 a__plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__plus(z, z') -{ 0 }-> 1 + a__plus(mark(z0), mark(z1)) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 a__plus(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 mark(z) -{ 0 }-> a__plus(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__and(a__plus(mark(z0108), mark(z172)), z1) :|: z0108 >= 0, z1 >= 0, z = 1 + (1 + z0108 + z172) + z1, z172 >= 0 mark(z) -{ 0 }-> a__and(a__and(mark(z0107), z171), z1) :|: z1 >= 0, z171 >= 0, z = 1 + (1 + z0107 + z171) + z1, z0107 >= 0 mark(z) -{ 0 }-> a__and(1, z1) :|: z1 >= 0, z = 1 + 1 + z1 mark(z) -{ 0 }-> a__and(0, z1) :|: z1 >= 0, z = 1 + 0 + z1 mark(z) -{ 0 }-> a__and(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__and(1 + mark(z0109), z1) :|: z1 >= 0, z0109 >= 0, z = 1 + (1 + z0109) + z1 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0 ---------------------------------------- (49) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (50) Obligation: Complexity RNTS consisting of the following rules: A__AND(z, z') -{ 1 }-> 1 + MARK(z') :|: z = 1, z' >= 0 A__PLUS(z, z') -{ 1 }-> 1 + MARK(z) :|: z >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__PLUS(mark(z), mark(z' - 1)) + MARK(z) :|: z' - 1 >= 0, z >= 0 A__PLUS(z, z') -{ 1 }-> 1 + A__PLUS(mark(z), mark(z' - 1)) + MARK(z' - 1) :|: z' - 1 >= 0, z >= 0 MARK(z) -{ 1 }-> 1 + MARK(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__AND(a__plus(mark(z042), mark(z128)), z1) + MARK(1 + z042 + z128) :|: z042 >= 0, z = 1 + (1 + z042 + z128) + z1, z1 >= 0, z128 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__and(mark(z041), z127), z1) + MARK(1 + z041 + z127) :|: z1 >= 0, z041 >= 0, z = 1 + (1 + z041 + z127) + z1, z127 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(1, z - 2) + MARK(1) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(0, z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__AND(0, z - 1) + MARK(0) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(1 + mark(z043), z1) + MARK(1 + z043) :|: z1 >= 0, z043 >= 0, z = 1 + (1 + z043) + z1 a__and(z, z') -{ 0 }-> mark(z') :|: z = 1, z' >= 0 a__and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__and(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__plus(z, z') -{ 0 }-> mark(z) :|: z >= 0, z' = 0 a__plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__plus(z, z') -{ 0 }-> 1 + a__plus(mark(z), mark(z' - 1)) :|: z' - 1 >= 0, z >= 0 a__plus(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 mark(z) -{ 0 }-> a__plus(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__and(a__plus(mark(z0108), mark(z172)), z1) :|: z0108 >= 0, z1 >= 0, z = 1 + (1 + z0108 + z172) + z1, z172 >= 0 mark(z) -{ 0 }-> a__and(a__and(mark(z0107), z171), z1) :|: z1 >= 0, z171 >= 0, z = 1 + (1 + z0107 + z171) + z1, z0107 >= 0 mark(z) -{ 0 }-> a__and(1, z - 2) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__and(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__and(0, z - 1) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__and(1 + mark(z0109), z1) :|: z1 >= 0, z0109 >= 0, z = 1 + (1 + z0109) + z1 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: z >= 0 mark(z) -{ 0 }-> 1 + mark(z - 1) :|: z - 1 >= 0 ---------------------------------------- (51) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: a__and(v0, v1) -> null_a__and [0] a__plus(v0, v1) -> null_a__plus [0] mark(v0) -> null_mark [0] A__AND(v0, v1) -> null_A__AND [0] A__PLUS(v0, v1) -> null_A__PLUS [0] MARK(v0) -> null_MARK [0] And the following fresh constants: null_a__and, null_a__plus, null_mark, null_A__AND, null_A__PLUS, null_MARK ---------------------------------------- (52) 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__AND(tt, z0) -> c(MARK(z0)) [1] A__PLUS(z0, 0) -> c2(MARK(z0)) [1] A__PLUS(z0, s(z1)) -> c3(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] A__PLUS(z0, s(z1)) -> c4(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) [1] MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(s(z0)) -> c11(MARK(z0)) [1] a__and(tt, z0) -> mark(z0) [0] a__and(z0, z1) -> and(z0, z1) [0] a__plus(z0, 0) -> mark(z0) [0] a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) [0] a__plus(z0, z1) -> plus(z0, z1) [0] mark(and(z0, z1)) -> a__and(mark(z0), z1) [0] mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0] mark(tt) -> tt [0] mark(0) -> 0 [0] mark(s(z0)) -> s(mark(z0)) [0] a__and(v0, v1) -> null_a__and [0] a__plus(v0, v1) -> null_a__plus [0] mark(v0) -> null_mark [0] A__AND(v0, v1) -> null_A__AND [0] A__PLUS(v0, v1) -> null_A__PLUS [0] MARK(v0) -> null_MARK [0] The TRS has the following type information: A__AND :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> c:null_A__AND tt :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark c :: c6:c7:c8:c11:null_MARK -> c:null_A__AND MARK :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> c6:c7:c8:c11:null_MARK A__PLUS :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> c2:c3:c4:null_A__PLUS 0 :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark c2 :: c6:c7:c8:c11:null_MARK -> c2:c3:c4:null_A__PLUS s :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> tt:0:s:and:plus:null_a__and:null_a__plus:null_mark c3 :: c2:c3:c4:null_A__PLUS -> c6:c7:c8:c11:null_MARK -> c2:c3:c4:null_A__PLUS mark :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> tt:0:s:and:plus:null_a__and:null_a__plus:null_mark c4 :: c2:c3:c4:null_A__PLUS -> c6:c7:c8:c11:null_MARK -> c2:c3:c4:null_A__PLUS and :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> tt:0:s:and:plus:null_a__and:null_a__plus:null_mark c6 :: c:null_A__AND -> c6:c7:c8:c11:null_MARK -> c6:c7:c8:c11:null_MARK plus :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> tt:0:s:and:plus:null_a__and:null_a__plus:null_mark c7 :: c2:c3:c4:null_A__PLUS -> c6:c7:c8:c11:null_MARK -> c6:c7:c8:c11:null_MARK c8 :: c2:c3:c4:null_A__PLUS -> c6:c7:c8:c11:null_MARK -> c6:c7:c8:c11:null_MARK c11 :: c6:c7:c8:c11:null_MARK -> c6:c7:c8:c11:null_MARK a__and :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> tt:0:s:and:plus:null_a__and:null_a__plus:null_mark a__plus :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> tt:0:s:and:plus:null_a__and:null_a__plus:null_mark -> tt:0:s:and:plus:null_a__and:null_a__plus:null_mark null_a__and :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark null_a__plus :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark null_mark :: tt:0:s:and:plus:null_a__and:null_a__plus:null_mark null_A__AND :: c:null_A__AND null_A__PLUS :: c2:c3:c4:null_A__PLUS null_MARK :: c6:c7:c8:c11:null_MARK Rewrite Strategy: INNERMOST ---------------------------------------- (53) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: tt => 1 0 => 0 null_a__and => 0 null_a__plus => 0 null_mark => 0 null_A__AND => 0 null_A__PLUS => 0 null_MARK => 0 ---------------------------------------- (54) Obligation: Complexity RNTS consisting of the following rules: A__AND(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__AND(z, z') -{ 1 }-> 1 + MARK(z0) :|: z = 1, z0 >= 0, z' = z0 A__PLUS(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__PLUS(z, z') -{ 1 }-> 1 + MARK(z0) :|: z = z0, z0 >= 0, z' = 0 A__PLUS(z, z') -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 A__PLUS(z, z') -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z1) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 MARK(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__AND(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__and(z, z') -{ 0 }-> mark(z0) :|: z = 1, z0 >= 0, z' = z0 a__and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__and(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__plus(z, z') -{ 0 }-> mark(z0) :|: z = z0, z0 >= 0, z' = 0 a__plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__plus(z, z') -{ 0 }-> 1 + a__plus(mark(z0), mark(z1)) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 a__plus(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 mark(z) -{ 0 }-> a__plus(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__and(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (55) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(z0, s(z1)) -> c3(A__PLUS(mark(z0), mark(z1)), MARK(z0)) by A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(A__PLUS(mark(x0), tt), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1)), MARK(tt)) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1)), MARK(0)) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) A__PLUS(z0, s(z1)) -> c4(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(A__PLUS(mark(x0), tt), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1)), MARK(tt)) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1)), MARK(0)) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) A__PLUS(z0, s(z1)) -> c4(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(A__PLUS(mark(x0), tt), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1)), MARK(tt)) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1)), MARK(0)) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c4_2, c6_2, c7_2, c8_2, c11_1, c3_2 ---------------------------------------- (57) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) A__PLUS(z0, s(z1)) -> c4(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) A__PLUS(z0, s(z1)) -> c4(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c4_2, c6_2, c7_2, c8_2, c11_1, c3_2, c3_1 ---------------------------------------- (59) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(z0, s(z1)) -> c4(A__PLUS(mark(z0), mark(z1)), MARK(z1)) by A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(tt)) -> c4(A__PLUS(mark(x0), tt), MARK(tt)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0), MARK(0)) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(tt)) -> c4(A__PLUS(mark(x0), tt), MARK(tt)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0), MARK(0)) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(tt)) -> c4(A__PLUS(mark(x0), tt), MARK(tt)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0), MARK(0)) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c6_2, c7_2, c8_2, c11_1, c3_2, c3_1, c4_2 ---------------------------------------- (61) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__PLUS(x0, s(tt)) -> c4(A__PLUS(mark(x0), tt), MARK(tt)) ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0), MARK(0)) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0), MARK(0)) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c6_2, c7_2, c8_2, c11_1, c3_2, c3_1, c4_2 ---------------------------------------- (63) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c6_2, c7_2, c8_2, c11_1, c3_2, c3_1, c4_2, c4_1 ---------------------------------------- (65) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(z0, z1)) -> c6(A__AND(mark(z0), z1), MARK(z0)) by MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1), MARK(tt)) MARK(and(0, x1)) -> c6(A__AND(0, x1), MARK(0)) MARK(and(s(z0), x1)) -> c6(A__AND(s(mark(z0)), x1), MARK(s(z0))) ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1), MARK(tt)) MARK(and(0, x1)) -> c6(A__AND(0, x1), MARK(0)) MARK(and(s(z0), x1)) -> c6(A__AND(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1), MARK(tt)) MARK(and(0, x1)) -> c6(A__AND(0, x1), MARK(0)) MARK(and(s(z0), x1)) -> c6(A__AND(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c7_2, c8_2, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2 ---------------------------------------- (67) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(and(0, x1)) -> c6(A__AND(0, x1), MARK(0)) ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c6(A__AND(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c6(A__AND(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c7_2, c8_2, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2 ---------------------------------------- (69) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c7_2, c8_2, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1 ---------------------------------------- (71) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(z0, z1)) -> c7(A__PLUS(mark(z0), mark(z1)), MARK(z0)) by MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, tt)) -> c7(A__PLUS(mark(x0), tt), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1)), MARK(tt)) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1)), MARK(0)) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, tt)) -> c7(A__PLUS(mark(x0), tt), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1)), MARK(tt)) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1)), MARK(0)) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, tt)) -> c7(A__PLUS(mark(x0), tt), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1)), MARK(tt)) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1)), MARK(0)) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c8_2, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2 ---------------------------------------- (73) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c8_2, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1 ---------------------------------------- (75) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(z0, z1)) -> c8(A__PLUS(mark(z0), mark(z1)), MARK(z1)) by MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, tt)) -> c8(A__PLUS(mark(x0), tt), MARK(tt)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, tt)) -> c8(A__PLUS(mark(x0), tt), MARK(tt)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, tt)) -> c8(A__PLUS(mark(x0), tt), MARK(tt)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2 ---------------------------------------- (77) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(x0, tt)) -> c8(A__PLUS(mark(x0), tt), MARK(tt)) ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2 ---------------------------------------- (79) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (81) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(x0, s(and(z0, z1))) -> c3(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) by A__PLUS(x0, s(and(x1, z1))) -> c3(A__PLUS(mark(x0), and(mark(x1), z1)), MARK(x0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2)), MARK(tt)) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2)), MARK(0)) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(x1, z1))) -> c3(A__PLUS(mark(x0), and(mark(x1), z1)), MARK(x0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2)), MARK(tt)) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2)), MARK(0)) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(x1, z1))) -> c3(A__PLUS(mark(x0), and(mark(x1), z1)), MARK(x0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2)), MARK(tt)) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2)), MARK(0)) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (83) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (85) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(x0, s(plus(z0, z1))) -> c3(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) by A__PLUS(x0, s(plus(x1, x2))) -> c3(A__PLUS(mark(x0), plus(mark(x1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(tt)) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(0)) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, x2))) -> c3(A__PLUS(mark(x0), plus(mark(x1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(tt)) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(0)) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, x2))) -> c3(A__PLUS(mark(x0), plus(mark(x1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(tt)) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(0)) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (87) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (89) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(x0, s(s(z0))) -> c3(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) by A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1))), MARK(tt)) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1))), MARK(0)) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1))), MARK(tt)) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1))), MARK(0)) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1))), MARK(tt)) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1))), MARK(0)) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (91) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (93) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(and(z0, z1), s(x1)) -> c3(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) by A__PLUS(and(x0, x1), s(and(z0, z1))) -> c3(A__PLUS(a__and(mark(x0), x1), a__and(mark(z0), z1)), MARK(and(x0, x1))) A__PLUS(and(x0, x1), s(plus(z0, z1))) -> c3(A__PLUS(a__and(mark(x0), x1), a__plus(mark(z0), mark(z1))), MARK(and(x0, x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(A__PLUS(a__and(mark(x0), x1), tt), MARK(and(x0, x1))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, x1), s(s(z0))) -> c3(A__PLUS(a__and(mark(x0), x1), s(mark(z0))), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2)), MARK(and(0, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(tt)) -> c3(A__PLUS(a__and(mark(x0), x1), tt), MARK(and(x0, x1))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2)), MARK(and(0, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(tt)) -> c3(A__PLUS(a__and(mark(x0), x1), tt), MARK(and(x0, x1))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2)), MARK(and(0, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (95) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (97) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(plus(z0, z1), s(x1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) by A__PLUS(plus(x0, x1), s(and(z0, z1))) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), a__and(mark(z0), z1)), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), tt), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(s(z0))) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(tt)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), tt), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(tt)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), tt), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (99) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (101) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) by A__PLUS(s(x0), s(and(z0, z1))) -> c3(A__PLUS(s(mark(x0)), a__and(mark(z0), z1)), MARK(s(x0))) A__PLUS(s(x0), s(plus(z0, z1))) -> c3(A__PLUS(s(mark(x0)), a__plus(mark(z0), mark(z1))), MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(A__PLUS(s(mark(x0)), tt), MARK(s(x0))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(x0), s(s(z0))) -> c3(A__PLUS(s(mark(x0)), s(mark(z0))), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(tt)) -> c3(A__PLUS(s(mark(x0)), tt), MARK(s(x0))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(tt)) -> c3(A__PLUS(s(mark(x0)), tt), MARK(s(x0))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (103) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (105) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) by A__PLUS(tt, s(and(z0, z1))) -> c3(A__PLUS(tt, a__and(mark(z0), z1))) A__PLUS(tt, s(plus(z0, z1))) -> c3(A__PLUS(tt, a__plus(mark(z0), mark(z1)))) A__PLUS(tt, s(tt)) -> c3(A__PLUS(tt, tt)) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(tt, s(s(z0))) -> c3(A__PLUS(tt, s(mark(z0)))) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(tt)) -> c3(A__PLUS(tt, tt)) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(tt)) -> c3(A__PLUS(tt, tt)) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (107) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__PLUS(tt, s(tt)) -> c3(A__PLUS(tt, tt)) ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (109) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) by A__PLUS(0, s(and(z0, z1))) -> c3(A__PLUS(0, a__and(mark(z0), z1))) A__PLUS(0, s(plus(z0, z1))) -> c3(A__PLUS(0, a__plus(mark(z0), mark(z1)))) A__PLUS(0, s(tt)) -> c3(A__PLUS(0, tt)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(0, s(s(z0))) -> c3(A__PLUS(0, s(mark(z0)))) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(tt)) -> c3(A__PLUS(0, tt)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(tt)) -> c3(A__PLUS(0, tt)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (111) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__PLUS(0, s(tt)) -> c3(A__PLUS(0, tt)) ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (113) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) by A__PLUS(x0, s(and(x1, z1))) -> c4(A__PLUS(mark(x0), and(mark(x1), z1)), MARK(and(x1, z1))) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2)), MARK(and(0, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(x1, z1))) -> c4(A__PLUS(mark(x0), and(mark(x1), z1)), MARK(and(x1, z1))) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2)), MARK(and(0, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(x1, z1))) -> c4(A__PLUS(mark(x0), and(mark(x1), z1)), MARK(and(x1, z1))) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2)), MARK(and(0, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (115) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (117) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) by A__PLUS(x0, s(plus(x1, x2))) -> c4(A__PLUS(mark(x0), plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(A__PLUS(mark(x0), plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(A__PLUS(mark(x0), plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (119) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (121) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(x0, s(s(z0))) -> c4(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) by A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (123) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(and(z0, z1), s(x1)) -> c4(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) by A__PLUS(and(x0, x1), s(and(z0, z1))) -> c4(A__PLUS(a__and(mark(x0), x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(and(x0, x1), s(plus(z0, z1))) -> c4(A__PLUS(a__and(mark(x0), x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(and(x0, x1), s(tt)) -> c4(A__PLUS(a__and(mark(x0), x1), tt), MARK(tt)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0), MARK(0)) A__PLUS(and(x0, x1), s(s(z0))) -> c4(A__PLUS(a__and(mark(x0), x1), s(mark(z0))), MARK(s(z0))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, x1), s(tt)) -> c4(A__PLUS(a__and(mark(x0), x1), tt), MARK(tt)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0), MARK(0)) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, x1), s(tt)) -> c4(A__PLUS(a__and(mark(x0), x1), tt), MARK(tt)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0), MARK(0)) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (125) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__PLUS(and(x0, x1), s(tt)) -> c4(A__PLUS(a__and(mark(x0), x1), tt), MARK(tt)) ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0), MARK(0)) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0), MARK(0)) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (127) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (129) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(plus(z0, z1), s(x1)) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) by A__PLUS(plus(x0, x1), s(and(z0, z1))) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(plus(x0, x1), s(plus(z0, z1))) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(plus(x0, x1), s(tt)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), tt), MARK(tt)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(0)) A__PLUS(plus(x0, x1), s(s(z0))) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(tt)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), tt), MARK(tt)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(tt)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), tt), MARK(tt)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (131) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__PLUS(plus(x0, x1), s(tt)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), tt), MARK(tt)) ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (133) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (135) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(tt, s(x1)) -> c4(A__PLUS(tt, mark(x1)), MARK(x1)) by A__PLUS(tt, s(and(z0, z1))) -> c4(A__PLUS(tt, a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(tt, s(plus(z0, z1))) -> c4(A__PLUS(tt, a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(tt, s(tt)) -> c4(A__PLUS(tt, tt), MARK(tt)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0), MARK(0)) A__PLUS(tt, s(s(z0))) -> c4(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, 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MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 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MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), 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0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(tt)) -> c4(A__PLUS(tt, tt), MARK(tt)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0), MARK(0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(tt)) -> c4(A__PLUS(tt, tt), MARK(tt)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0), MARK(0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (137) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__PLUS(tt, s(tt)) -> c4(A__PLUS(tt, tt), MARK(tt)) ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0), MARK(0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0), MARK(0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (139) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (141) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(0, s(x1)) -> c4(A__PLUS(0, mark(x1)), MARK(x1)) by A__PLUS(0, s(and(z0, z1))) -> c4(A__PLUS(0, a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(0, s(plus(z0, z1))) -> c4(A__PLUS(0, a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(0, s(tt)) -> c4(A__PLUS(0, tt), MARK(tt)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0), MARK(0)) A__PLUS(0, s(s(z0))) -> c4(A__PLUS(0, s(mark(z0))), MARK(s(z0))) ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(tt)) -> c4(A__PLUS(0, tt), MARK(tt)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0), MARK(0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(tt)) -> c4(A__PLUS(0, tt), MARK(tt)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0), MARK(0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (143) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__PLUS(0, s(tt)) -> c4(A__PLUS(0, tt), MARK(tt)) ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0), MARK(0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0), MARK(0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (145) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_2, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1 ---------------------------------------- (147) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(s(z0), s(x1)) -> c4(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) by A__PLUS(s(x0), s(and(z0, z1))) -> c4(A__PLUS(s(mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(s(x0), s(plus(z0, z1))) -> c4(A__PLUS(s(mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(s(x0), s(tt)) -> c4(A__PLUS(s(mark(x0)), tt), MARK(tt)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0), MARK(0)) A__PLUS(s(x0), s(s(z0))) -> c4(A__PLUS(s(mark(x0)), s(mark(z0))), MARK(s(z0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(x0), s(tt)) -> c4(A__PLUS(s(mark(x0)), tt), MARK(tt)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0), MARK(0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(x0), s(tt)) -> c4(A__PLUS(s(mark(x0)), tt), MARK(tt)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0), MARK(0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2 ---------------------------------------- (149) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__PLUS(s(x0), s(tt)) -> c4(A__PLUS(s(mark(x0)), tt), MARK(tt)) ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0), MARK(0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0), MARK(0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2 ---------------------------------------- (151) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2 ---------------------------------------- (153) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(and(z0, z1), x1)) -> c6(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) by MARK(and(and(x0, z1), x2)) -> c6(A__AND(and(mark(x0), z1), x2), MARK(and(x0, z1))) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2), MARK(and(0, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(x0, z1), x2)) -> c6(A__AND(and(mark(x0), z1), x2), MARK(and(x0, z1))) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2), MARK(and(0, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(x0, z1), x2)) -> c6(A__AND(and(mark(x0), z1), x2), MARK(and(x0, z1))) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2), MARK(and(0, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2 ---------------------------------------- (155) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_2, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2 ---------------------------------------- (157) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(plus(z0, z1), x1)) -> c6(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) by MARK(and(plus(x0, x1), x2)) -> c6(A__AND(plus(mark(x0), mark(x1)), x2), MARK(plus(x0, x1))) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, x1), x2)) -> c6(A__AND(plus(mark(x0), mark(x1)), x2), MARK(plus(x0, x1))) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, 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MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, x1), x2)) -> c6(A__AND(plus(mark(x0), mark(x1)), x2), MARK(plus(x0, x1))) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (159) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (161) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(x0, and(z0, z1))) -> c7(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) by MARK(plus(x0, and(x1, z1))) -> c7(A__PLUS(mark(x0), and(mark(x1), z1)), MARK(x0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2)), MARK(tt)) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2)), MARK(0)) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) ---------------------------------------- (162) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(x1, z1))) -> c7(A__PLUS(mark(x0), and(mark(x1), z1)), MARK(x0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2)), MARK(tt)) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2)), MARK(0)) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(x1, z1))) -> c7(A__PLUS(mark(x0), and(mark(x1), z1)), MARK(x0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2)), MARK(tt)) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2)), MARK(0)) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (163) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), 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MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (165) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(x0, plus(z0, z1))) -> c7(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) by MARK(plus(x0, plus(x1, x2))) -> c7(A__PLUS(mark(x0), plus(mark(x1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(tt)) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(0)) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) ---------------------------------------- (166) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, 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c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, x2))) -> c7(A__PLUS(mark(x0), plus(mark(x1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(tt)) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(0)) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, x2))) -> c7(A__PLUS(mark(x0), plus(mark(x1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(tt)) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(0)) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (167) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (168) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) 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MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), 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x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (169) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(x0, s(z0))) -> c7(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) by MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1))), MARK(tt)) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1))), MARK(0)) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) ---------------------------------------- (170) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), 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c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1))), MARK(tt)) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1))), MARK(0)) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1))), MARK(tt)) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1))), MARK(0)) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (171) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (172) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), 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a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (173) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(and(z0, z1), x1)) -> c7(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) by MARK(plus(and(x0, x1), and(z0, z1))) -> c7(A__PLUS(a__and(mark(x0), x1), a__and(mark(z0), z1)), MARK(and(x0, x1))) MARK(plus(and(x0, x1), plus(z0, z1))) -> c7(A__PLUS(a__and(mark(x0), x1), a__plus(mark(z0), mark(z1))), MARK(and(x0, x1))) MARK(plus(and(x0, x1), tt)) -> c7(A__PLUS(a__and(mark(x0), x1), tt), MARK(and(x0, x1))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, x1), s(z0))) -> c7(A__PLUS(a__and(mark(x0), x1), s(mark(z0))), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2)), MARK(and(0, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) ---------------------------------------- (174) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), tt)) -> c7(A__PLUS(a__and(mark(x0), x1), tt), MARK(and(x0, x1))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2)), MARK(and(0, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), tt)) -> c7(A__PLUS(a__and(mark(x0), x1), tt), MARK(and(x0, x1))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2)), MARK(and(0, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (175) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (176) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (177) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(plus(z0, z1), x1)) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) by MARK(plus(plus(x0, x1), and(z0, z1))) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), a__and(mark(z0), z1)), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), plus(z0, z1))) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), tt)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), tt), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), s(z0))) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) ---------------------------------------- (178) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), tt)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), tt), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), 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x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), tt)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), tt), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (179) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (180) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (181) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(s(z0), x1)) -> c7(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) by MARK(plus(s(x0), and(z0, z1))) -> c7(A__PLUS(s(mark(x0)), a__and(mark(z0), z1)), MARK(s(x0))) MARK(plus(s(x0), plus(z0, z1))) -> c7(A__PLUS(s(mark(x0)), a__plus(mark(z0), mark(z1))), MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(A__PLUS(s(mark(x0)), tt), MARK(s(x0))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(x0), s(z0))) -> c7(A__PLUS(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) ---------------------------------------- (182) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) 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a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), tt)) -> c7(A__PLUS(s(mark(x0)), tt), MARK(s(x0))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), tt)) -> c7(A__PLUS(s(mark(x0)), tt), MARK(s(x0))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (183) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (184) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (185) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(tt, x1)) -> c7(A__PLUS(tt, mark(x1))) by MARK(plus(tt, and(z0, z1))) -> c7(A__PLUS(tt, a__and(mark(z0), z1))) MARK(plus(tt, plus(z0, z1))) -> c7(A__PLUS(tt, a__plus(mark(z0), mark(z1)))) MARK(plus(tt, tt)) -> c7(A__PLUS(tt, tt)) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(tt, s(z0))) -> c7(A__PLUS(tt, s(mark(z0)))) ---------------------------------------- (186) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> 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A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) 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MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, 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c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> 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MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, tt)) -> c7(A__PLUS(tt, tt)) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (187) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(tt, tt)) -> c7(A__PLUS(tt, tt)) ---------------------------------------- (188) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> 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x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (189) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(0, x1)) -> c7(A__PLUS(0, mark(x1))) by MARK(plus(0, and(z0, z1))) -> c7(A__PLUS(0, a__and(mark(z0), z1))) MARK(plus(0, plus(z0, z1))) -> c7(A__PLUS(0, a__plus(mark(z0), mark(z1)))) MARK(plus(0, tt)) -> c7(A__PLUS(0, tt)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(0, s(z0))) -> c7(A__PLUS(0, s(mark(z0)))) ---------------------------------------- (190) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, 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c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), 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a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, tt)) -> c7(A__PLUS(0, tt)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), 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c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, tt)) -> c7(A__PLUS(0, tt)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (191) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(0, tt)) -> c7(A__PLUS(0, tt)) ---------------------------------------- (192) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> 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mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (193) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(x0, and(z0, z1))) -> c8(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) by MARK(plus(x0, and(x1, z1))) -> c8(A__PLUS(mark(x0), and(mark(x1), z1)), MARK(and(x1, z1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2)), MARK(and(0, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) ---------------------------------------- (194) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(x1, z1))) -> c8(A__PLUS(mark(x0), and(mark(x1), z1)), MARK(and(x1, z1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2)), MARK(and(0, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(x1, z1))) -> c8(A__PLUS(mark(x0), and(mark(x1), z1)), MARK(and(x1, z1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2)), MARK(and(0, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (195) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (196) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, 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c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 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c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> 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c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), 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c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), 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c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (197) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(x0, plus(z0, z1))) -> c8(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) by MARK(plus(x0, plus(x1, x2))) -> c8(A__PLUS(mark(x0), plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) ---------------------------------------- (198) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(A__PLUS(mark(x0), plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(A__PLUS(mark(x0), plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (199) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (200) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) 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MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) 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0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (201) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(x0, s(z0))) -> c8(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) by MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) ---------------------------------------- (202) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) 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x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) 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MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (203) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(and(z0, z1), x1)) -> c8(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) by MARK(plus(and(x0, x1), and(z0, z1))) -> c8(A__PLUS(a__and(mark(x0), x1), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(and(x0, x1), plus(z0, z1))) -> c8(A__PLUS(a__and(mark(x0), x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(and(x0, x1), tt)) -> c8(A__PLUS(a__and(mark(x0), x1), tt), MARK(tt)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0), MARK(0)) MARK(plus(and(x0, x1), s(z0))) -> c8(A__PLUS(a__and(mark(x0), x1), s(mark(z0))), MARK(s(z0))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) ---------------------------------------- (204) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, x1), tt)) -> c8(A__PLUS(a__and(mark(x0), x1), tt), MARK(tt)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0), MARK(0)) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, 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plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, x1), tt)) -> c8(A__PLUS(a__and(mark(x0), x1), tt), MARK(tt)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0), MARK(0)) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (205) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(and(x0, x1), tt)) -> c8(A__PLUS(a__and(mark(x0), x1), tt), MARK(tt)) ---------------------------------------- (206) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) 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MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, 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c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) 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x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0), MARK(0)) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (207) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (208) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), 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MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), 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c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, 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MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), 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x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (209) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(plus(z0, z1), x1)) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) by MARK(plus(plus(x0, x1), and(z0, z1))) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(plus(x0, x1), plus(z0, z1))) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(plus(x0, x1), tt)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), tt), MARK(tt)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(0)) MARK(plus(plus(x0, x1), s(z0))) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) ---------------------------------------- (210) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), 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c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, 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MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), 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mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), tt)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), tt), MARK(tt)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) 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MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, 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MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), tt)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), tt), MARK(tt)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (211) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(plus(x0, x1), tt)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), tt), MARK(tt)) ---------------------------------------- (212) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) 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plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) 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MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (213) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (214) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, 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MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> 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MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, 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c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) 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x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (215) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(tt, x1)) -> c8(A__PLUS(tt, mark(x1)), MARK(x1)) by MARK(plus(tt, and(z0, z1))) -> c8(A__PLUS(tt, a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(tt, plus(z0, z1))) -> c8(A__PLUS(tt, a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(tt, tt)) -> c8(A__PLUS(tt, tt), MARK(tt)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0), MARK(0)) MARK(plus(tt, s(z0))) -> c8(A__PLUS(tt, s(mark(z0))), MARK(s(z0))) ---------------------------------------- (216) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, 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c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, tt)) -> c8(A__PLUS(tt, tt), MARK(tt)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0), MARK(0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, tt)) -> c8(A__PLUS(tt, tt), MARK(tt)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0), MARK(0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (217) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(tt, tt)) -> c8(A__PLUS(tt, tt), MARK(tt)) ---------------------------------------- (218) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 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mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0), MARK(0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, 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MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), 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c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) 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a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0), MARK(0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (219) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (220) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, 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MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) 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c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, 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MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 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mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (221) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(0, x1)) -> c8(A__PLUS(0, mark(x1)), MARK(x1)) by MARK(plus(0, and(z0, z1))) -> c8(A__PLUS(0, a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(0, plus(z0, z1))) -> c8(A__PLUS(0, a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(0, tt)) -> c8(A__PLUS(0, tt), MARK(tt)) MARK(plus(0, 0)) -> c8(A__PLUS(0, 0), MARK(0)) MARK(plus(0, s(z0))) -> c8(A__PLUS(0, s(mark(z0))), MARK(s(z0))) ---------------------------------------- (222) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) 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mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0)) MARK(plus(0, tt)) -> c8(A__PLUS(0, tt), MARK(tt)) MARK(plus(0, 0)) -> c8(A__PLUS(0, 0), MARK(0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (223) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(0, tt)) -> c8(A__PLUS(0, tt), MARK(tt)) ---------------------------------------- (224) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), 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a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c8(A__PLUS(0, 0), MARK(0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> 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z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c8(A__PLUS(0, 0), MARK(0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (225) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (226) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> 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MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c8(A__PLUS(0, 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_2, c8_1, c4_2, c6_2 ---------------------------------------- (227) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(s(z0), x1)) -> c8(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) by MARK(plus(s(x0), and(z0, z1))) -> c8(A__PLUS(s(mark(x0)), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(s(x0), plus(z0, z1))) -> c8(A__PLUS(s(mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(s(x0), tt)) -> c8(A__PLUS(s(mark(x0)), tt), MARK(tt)) MARK(plus(s(x0), 0)) -> c8(A__PLUS(s(mark(x0)), 0), MARK(0)) MARK(plus(s(x0), s(z0))) -> c8(A__PLUS(s(mark(x0)), s(mark(z0))), MARK(s(z0))) MARK(plus(s(and(z0, z1)), x1)) -> c8(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(plus(s(plus(z0, z1)), x1)) -> c8(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(plus(s(tt), x1)) -> c8(A__PLUS(s(tt), mark(x1)), MARK(x1)) MARK(plus(s(0), x1)) -> c8(A__PLUS(s(0), mark(x1)), MARK(x1)) MARK(plus(s(s(z0)), x1)) -> c8(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) ---------------------------------------- (228) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) 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c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> 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c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c8(A__PLUS(0, 0)) MARK(plus(s(x0), tt)) -> c8(A__PLUS(s(mark(x0)), tt), MARK(tt)) MARK(plus(s(x0), 0)) -> c8(A__PLUS(s(mark(x0)), 0), MARK(0)) MARK(plus(s(and(z0, z1)), x1)) -> c8(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(plus(s(plus(z0, z1)), x1)) -> c8(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(plus(s(tt), x1)) -> c8(A__PLUS(s(tt), mark(x1)), MARK(x1)) MARK(plus(s(0), x1)) -> c8(A__PLUS(s(0), mark(x1)), MARK(x1)) MARK(plus(s(s(z0)), x1)) -> c8(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_1, c4_2, c6_2, c8_2 ---------------------------------------- (229) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(s(x0), tt)) -> c8(A__PLUS(s(mark(x0)), tt), MARK(tt)) ---------------------------------------- (230) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> 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MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c8(A__PLUS(0, 0)) MARK(plus(s(x0), 0)) -> c8(A__PLUS(s(mark(x0)), 0), MARK(0)) MARK(plus(s(and(z0, z1)), x1)) -> c8(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(plus(s(plus(z0, z1)), x1)) -> c8(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(plus(s(tt), x1)) -> c8(A__PLUS(s(tt), mark(x1)), MARK(x1)) MARK(plus(s(0), x1)) -> c8(A__PLUS(s(0), mark(x1)), MARK(x1)) MARK(plus(s(s(z0)), x1)) -> c8(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c8(A__PLUS(0, 0)) MARK(plus(s(x0), 0)) -> c8(A__PLUS(s(mark(x0)), 0), MARK(0)) MARK(plus(s(and(z0, z1)), x1)) -> c8(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(plus(s(plus(z0, z1)), x1)) -> c8(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(plus(s(tt), x1)) -> c8(A__PLUS(s(tt), mark(x1)), MARK(x1)) MARK(plus(s(0), x1)) -> c8(A__PLUS(s(0), mark(x1)), MARK(x1)) MARK(plus(s(s(z0)), x1)) -> c8(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_1, c4_2, c6_2, c8_2 ---------------------------------------- (231) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (232) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) 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c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c8(A__PLUS(0, 0)) MARK(plus(s(and(z0, z1)), x1)) -> c8(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(plus(s(plus(z0, z1)), x1)) -> c8(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(plus(s(tt), x1)) -> c8(A__PLUS(s(tt), mark(x1)), MARK(x1)) MARK(plus(s(0), x1)) -> c8(A__PLUS(s(0), mark(x1)), MARK(x1)) MARK(plus(s(s(z0)), x1)) -> c8(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(plus(s(x0), 0)) -> c8(A__PLUS(s(mark(x0)), 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_1, c4_2, c6_2, c8_2 ---------------------------------------- (233) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(and(0, x1), x2)) -> c6(A__AND(a__and(0, x1), x2)) by MARK(and(and(0, z1), x1)) -> c6(A__AND(and(0, z1), x1)) ---------------------------------------- (234) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) 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c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c8(A__PLUS(0, 0)) MARK(plus(s(and(z0, z1)), x1)) -> c8(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(plus(s(plus(z0, z1)), x1)) -> c8(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(plus(s(tt), x1)) -> c8(A__PLUS(s(tt), mark(x1)), MARK(x1)) MARK(plus(s(0), x1)) -> c8(A__PLUS(s(0), mark(x1)), MARK(x1)) MARK(plus(s(s(z0)), x1)) -> c8(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(plus(s(x0), 0)) -> c8(A__PLUS(s(mark(x0)), 0)) MARK(and(and(0, z1), x1)) -> c6(A__AND(and(0, z1), x1)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c8(A__PLUS(0, 0)) MARK(plus(s(and(z0, z1)), x1)) -> c8(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(plus(s(plus(z0, z1)), x1)) -> c8(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(plus(s(tt), x1)) -> c8(A__PLUS(s(tt), mark(x1)), MARK(x1)) MARK(plus(s(0), x1)) -> c8(A__PLUS(s(0), mark(x1)), MARK(x1)) MARK(plus(s(s(z0)), x1)) -> c8(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(plus(s(x0), 0)) -> c8(A__PLUS(s(mark(x0)), 0)) MARK(and(and(0, z1), x1)) -> c6(A__AND(and(0, z1), x1)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_1, c4_2, c6_2, c8_2 ---------------------------------------- (235) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(and(and(0, z1), x1)) -> c6(A__AND(and(0, z1), x1)) ---------------------------------------- (236) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), 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c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, 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MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c8(A__PLUS(0, 0)) MARK(plus(s(and(z0, z1)), x1)) -> c8(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(plus(s(plus(z0, z1)), x1)) -> c8(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(plus(s(tt), x1)) -> c8(A__PLUS(s(tt), mark(x1)), MARK(x1)) MARK(plus(s(0), x1)) -> c8(A__PLUS(s(0), mark(x1)), MARK(x1)) MARK(plus(s(s(z0)), x1)) -> c8(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(plus(s(x0), 0)) -> c8(A__PLUS(s(mark(x0)), 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c11(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x0, s(tt)) -> c3(MARK(x0)) A__PLUS(x0, s(0)) -> c4(A__PLUS(mark(x0), 0)) MARK(and(tt, x1)) -> c6(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c6(MARK(s(z0))) MARK(plus(x0, 0)) -> c7(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, tt)) -> c7(MARK(x0)) MARK(plus(x0, 0)) -> c8(A__PLUS(mark(x0), 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(tt, x2))) -> c3(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) A__PLUS(x0, s(and(0, x2))) -> c3(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) A__PLUS(x0, s(and(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) A__PLUS(s(z0), s(and(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) A__PLUS(x0, s(and(x1, z1))) -> c3(MARK(x0)) A__PLUS(tt, s(and(x1, x2))) -> c3(A__PLUS(tt, a__and(mark(x1), x2))) A__PLUS(0, s(and(x1, x2))) -> c3(A__PLUS(0, a__and(mark(x1), x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(plus(x1, 0))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(plus(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(tt, x2))) -> c3(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(0, x2))) -> c3(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(plus(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(plus(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(plus(x1, x2))) -> c3(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(s(and(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(s(plus(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(s(tt))) -> c3(A__PLUS(mark(x0), s(tt)), MARK(x0)) A__PLUS(x0, s(s(0))) -> c3(A__PLUS(mark(x0), s(0)), MARK(x0)) A__PLUS(x0, s(s(s(z0)))) -> c3(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) A__PLUS(and(z0, z1), s(s(x1))) -> c3(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) A__PLUS(s(z0), s(s(x1))) -> c3(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) A__PLUS(tt, s(s(x1))) -> c3(A__PLUS(tt, s(mark(x1)))) A__PLUS(0, s(s(x1))) -> c3(A__PLUS(0, s(mark(x1)))) A__PLUS(and(x0, x1), s(0)) -> c3(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) A__PLUS(and(x0, z1), s(x2)) -> c3(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(tt, x1), s(x2)) -> c3(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) A__PLUS(and(s(z0), x1), s(x2)) -> c3(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) A__PLUS(and(x0, x1), s(tt)) -> c3(MARK(and(x0, x1))) A__PLUS(and(0, x1), s(x2)) -> c3(A__PLUS(a__and(0, x1), mark(x2))) A__PLUS(plus(x0, x1), s(0)) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) A__PLUS(plus(x0, x1), s(x2)) -> c3(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__PLUS(plus(x0, tt), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) A__PLUS(plus(x0, 0), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) A__PLUS(plus(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(tt, x1), s(x2)) -> c3(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) A__PLUS(plus(0, x1), s(x2)) -> c3(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) A__PLUS(plus(s(z0), x1), s(x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) A__PLUS(plus(x0, x1), s(tt)) -> c3(MARK(plus(x0, x1))) A__PLUS(s(x0), s(0)) -> c3(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) A__PLUS(s(and(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) A__PLUS(s(plus(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(tt), s(x1)) -> c3(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) A__PLUS(s(0), s(x1)) -> c3(A__PLUS(s(0), mark(x1)), MARK(s(0))) A__PLUS(s(s(z0)), s(x1)) -> c3(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) A__PLUS(s(x0), s(x1)) -> c3(MARK(s(x0))) A__PLUS(s(x0), s(tt)) -> c3(MARK(s(x0))) A__PLUS(tt, s(0)) -> c3(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c3(A__PLUS(0, 0)) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(tt, x2))) -> c4(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) A__PLUS(x0, s(and(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) A__PLUS(and(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(tt, s(and(x1, x2))) -> c4(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(0, s(and(x1, x2))) -> c4(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(s(z0), s(and(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(x0, s(and(x1, z1))) -> c4(MARK(and(x1, z1))) A__PLUS(x0, s(and(0, x2))) -> c4(A__PLUS(mark(x0), a__and(0, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, tt))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) A__PLUS(x0, s(plus(x1, 0))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) A__PLUS(x0, s(plus(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) A__PLUS(x0, s(plus(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) A__PLUS(x0, s(plus(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) A__PLUS(x0, s(plus(tt, x2))) -> c4(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) A__PLUS(x0, s(plus(0, x2))) -> c4(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) A__PLUS(x0, s(plus(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> c4(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(0, s(plus(x1, x2))) -> c4(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(s(z0), s(plus(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(s(and(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) A__PLUS(x0, s(s(plus(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(tt))) -> c4(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) A__PLUS(x0, s(s(0))) -> c4(A__PLUS(mark(x0), s(0)), MARK(s(0))) A__PLUS(x0, s(s(s(z0)))) -> c4(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) A__PLUS(and(z0, z1), s(s(x1))) -> c4(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) A__PLUS(plus(z0, z1), s(s(x1))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) A__PLUS(tt, s(s(x1))) -> c4(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) A__PLUS(0, s(s(x1))) -> c4(A__PLUS(0, s(mark(x1))), MARK(s(x1))) A__PLUS(s(z0), s(s(x1))) -> c4(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) A__PLUS(x0, s(s(x1))) -> c4(MARK(s(x1))) A__PLUS(and(x0, z1), s(x2)) -> c4(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) A__PLUS(and(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) A__PLUS(and(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) A__PLUS(and(tt, x1), s(x2)) -> c4(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) A__PLUS(and(0, x1), s(x2)) -> c4(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) A__PLUS(and(s(z0), x1), s(x2)) -> c4(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) A__PLUS(and(x0, x1), s(0)) -> c4(A__PLUS(a__and(mark(x0), x1), 0)) A__PLUS(plus(x0, x1), s(x2)) -> c4(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(plus(x0, tt), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(plus(x0, 0), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(plus(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(plus(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(tt, x1), s(x2)) -> c4(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(0, x1), s(x2)) -> c4(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(s(z0), x1), s(x2)) -> c4(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(plus(x0, x1), s(0)) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) A__PLUS(tt, s(0)) -> c4(A__PLUS(tt, 0)) A__PLUS(0, s(0)) -> c4(A__PLUS(0, 0)) A__PLUS(s(and(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) A__PLUS(s(plus(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__PLUS(s(tt), s(x1)) -> c4(A__PLUS(s(tt), mark(x1)), MARK(x1)) A__PLUS(s(0), s(x1)) -> c4(A__PLUS(s(0), mark(x1)), MARK(x1)) A__PLUS(s(s(z0)), s(x1)) -> c4(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) A__PLUS(s(x0), s(0)) -> c4(A__PLUS(s(mark(x0)), 0)) MARK(and(and(and(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__and(mark(z0), z1), x1), x2), MARK(and(and(z0, z1), x1))) MARK(and(and(plus(z0, z1), x1), x2)) -> c6(A__AND(a__and(a__plus(mark(z0), mark(z1)), x1), x2), MARK(and(plus(z0, z1), x1))) MARK(and(and(tt, x1), x2)) -> c6(A__AND(a__and(tt, x1), x2), MARK(and(tt, x1))) MARK(and(and(s(z0), x1), x2)) -> c6(A__AND(a__and(s(mark(z0)), x1), x2), MARK(and(s(z0), x1))) MARK(and(and(x0, z1), x2)) -> c6(MARK(and(x0, z1))) MARK(and(plus(x0, and(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__and(mark(z0), z1)), x2), MARK(plus(x0, and(z0, z1)))) MARK(and(plus(x0, plus(z0, z1)), x2)) -> c6(A__AND(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), x2), MARK(plus(x0, plus(z0, z1)))) MARK(and(plus(x0, tt), x2)) -> c6(A__AND(a__plus(mark(x0), tt), x2), MARK(plus(x0, tt))) MARK(and(plus(x0, 0), x2)) -> c6(A__AND(a__plus(mark(x0), 0), x2), MARK(plus(x0, 0))) MARK(and(plus(x0, s(z0)), x2)) -> c6(A__AND(a__plus(mark(x0), s(mark(z0))), x2), MARK(plus(x0, s(z0)))) MARK(and(plus(and(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__and(mark(z0), z1), mark(x1)), x2), MARK(plus(and(z0, z1), x1))) MARK(and(plus(plus(z0, z1), x1), x2)) -> c6(A__AND(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), x2), MARK(plus(plus(z0, z1), x1))) MARK(and(plus(tt, x1), x2)) -> c6(A__AND(a__plus(tt, mark(x1)), x2), MARK(plus(tt, x1))) MARK(and(plus(0, x1), x2)) -> c6(A__AND(a__plus(0, mark(x1)), x2), MARK(plus(0, x1))) MARK(and(plus(s(z0), x1), x2)) -> c6(A__AND(a__plus(s(mark(z0)), mark(x1)), x2), MARK(plus(s(z0), x1))) MARK(and(plus(x0, x1), x2)) -> c6(MARK(plus(x0, x1))) MARK(plus(x0, and(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(x0)) MARK(plus(x0, and(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(plus(x0, and(tt, x2))) -> c7(A__PLUS(mark(x0), a__and(tt, x2)), MARK(x0)) MARK(plus(x0, and(0, x2))) -> c7(A__PLUS(mark(x0), a__and(0, x2)), MARK(x0)) MARK(plus(x0, and(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(x0)) MARK(plus(and(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(plus(z0, z1))) MARK(plus(s(z0), and(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(s(z0))) MARK(plus(x0, and(x1, z1))) -> c7(MARK(x0)) MARK(plus(tt, and(x1, x2))) -> c7(A__PLUS(tt, a__and(mark(x1), x2))) MARK(plus(0, and(x1, x2))) -> c7(A__PLUS(0, a__and(mark(x1), x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, plus(x1, tt))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(x0)) MARK(plus(x0, plus(x1, 0))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(x0)) MARK(plus(x0, plus(x1, s(z0)))) -> c7(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(x0)) MARK(plus(x0, plus(and(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(x0)) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c7(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(plus(x0, plus(tt, x2))) -> c7(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(x0)) MARK(plus(x0, plus(0, x2))) -> c7(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(x0)) MARK(plus(x0, plus(s(z0), x2))) -> c7(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(x0)) MARK(plus(and(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(z0, z1))) MARK(plus(s(z0), plus(x1, x2))) -> c7(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(s(z0))) MARK(plus(x0, plus(x1, x2))) -> c7(MARK(x0)) MARK(plus(tt, plus(x1, x2))) -> c7(A__PLUS(tt, a__plus(mark(x1), mark(x2)))) MARK(plus(0, plus(x1, x2))) -> c7(A__PLUS(0, a__plus(mark(x1), mark(x2)))) MARK(plus(x0, s(and(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(x0)) MARK(plus(x0, s(plus(z0, z1)))) -> c7(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(x0)) MARK(plus(x0, s(tt))) -> c7(A__PLUS(mark(x0), s(tt)), MARK(x0)) MARK(plus(x0, s(0))) -> c7(A__PLUS(mark(x0), s(0)), MARK(x0)) MARK(plus(x0, s(s(z0)))) -> c7(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(x0)) MARK(plus(and(z0, z1), s(x1))) -> c7(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), s(x1))) -> c7(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(plus(z0, z1))) MARK(plus(s(z0), s(x1))) -> c7(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(z0))) MARK(plus(tt, s(x1))) -> c7(A__PLUS(tt, s(mark(x1)))) MARK(plus(0, s(x1))) -> c7(A__PLUS(0, s(mark(x1)))) MARK(plus(and(x0, x1), 0)) -> c7(A__PLUS(a__and(mark(x0), x1), 0), MARK(and(x0, x1))) MARK(plus(and(x0, z1), x2)) -> c7(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(and(x0, z1))) MARK(plus(and(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(and(and(z0, z1), x1))) MARK(plus(and(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(plus(z0, z1), x1))) MARK(plus(and(tt, x1), x2)) -> c7(A__PLUS(a__and(tt, x1), mark(x2)), MARK(and(tt, x1))) MARK(plus(and(s(z0), x1), x2)) -> c7(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(and(s(z0), x1))) MARK(plus(and(x0, x1), tt)) -> c7(MARK(and(x0, x1))) MARK(plus(and(0, x1), x2)) -> c7(A__PLUS(a__and(0, x1), mark(x2))) MARK(plus(plus(x0, x1), 0)) -> c7(A__PLUS(a__plus(mark(x0), mark(x1)), 0), MARK(plus(x0, x1))) MARK(plus(plus(x0, x1), x2)) -> c7(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(plus(x0, x1))) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(plus(x0, and(z0, z1)))) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c7(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) MARK(plus(plus(x0, tt), x2)) -> c7(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(plus(x0, tt))) MARK(plus(plus(x0, 0), x2)) -> c7(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(plus(x0, 0))) MARK(plus(plus(x0, s(z0)), x2)) -> c7(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(plus(x0, s(z0)))) MARK(plus(plus(and(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c7(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) MARK(plus(plus(tt, x1), x2)) -> c7(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(plus(tt, x1))) MARK(plus(plus(0, x1), x2)) -> c7(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(plus(0, x1))) MARK(plus(plus(s(z0), x1), x2)) -> c7(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(plus(s(z0), x1))) MARK(plus(plus(x0, x1), tt)) -> c7(MARK(plus(x0, x1))) MARK(plus(s(x0), 0)) -> c7(A__PLUS(s(mark(x0)), 0), MARK(s(x0))) MARK(plus(s(and(z0, z1)), x1)) -> c7(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(s(and(z0, z1)))) MARK(plus(s(plus(z0, z1)), x1)) -> c7(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) MARK(plus(s(tt), x1)) -> c7(A__PLUS(s(tt), mark(x1)), MARK(s(tt))) MARK(plus(s(0), x1)) -> c7(A__PLUS(s(0), mark(x1)), MARK(s(0))) MARK(plus(s(s(z0)), x1)) -> c7(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(plus(s(x0), x1)) -> c7(MARK(s(x0))) MARK(plus(s(x0), tt)) -> c7(MARK(s(x0))) MARK(plus(tt, 0)) -> c7(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c7(A__PLUS(0, 0)) MARK(plus(x0, and(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) MARK(plus(x0, and(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) MARK(plus(x0, and(tt, x2))) -> c8(A__PLUS(mark(x0), a__and(tt, x2)), MARK(and(tt, x2))) MARK(plus(x0, and(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__and(s(mark(z0)), x2)), MARK(and(s(z0), x2))) MARK(plus(and(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(plus(z0, z1), and(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(tt, and(x1, x2))) -> c8(A__PLUS(tt, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(0, and(x1, x2))) -> c8(A__PLUS(0, a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(s(z0), and(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__and(mark(x1), x2)), MARK(and(x1, x2))) MARK(plus(x0, and(x1, z1))) -> c8(MARK(and(x1, z1))) MARK(plus(x0, and(0, x2))) -> c8(A__PLUS(mark(x0), a__and(0, x2))) MARK(plus(x0, plus(x1, and(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) MARK(plus(x0, plus(x1, plus(z0, z1)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) MARK(plus(x0, plus(x1, tt))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), tt)), MARK(plus(x1, tt))) MARK(plus(x0, plus(x1, 0))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), 0)), MARK(plus(x1, 0))) MARK(plus(x0, plus(x1, s(z0)))) -> c8(A__PLUS(mark(x0), a__plus(mark(x1), s(mark(z0)))), MARK(plus(x1, s(z0)))) MARK(plus(x0, plus(and(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), MARK(plus(and(z0, z1), x2))) MARK(plus(x0, plus(plus(z0, z1), x2))) -> c8(A__PLUS(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(plus(plus(z0, z1), x2))) MARK(plus(x0, plus(tt, x2))) -> c8(A__PLUS(mark(x0), a__plus(tt, mark(x2))), MARK(plus(tt, x2))) MARK(plus(x0, plus(0, x2))) -> c8(A__PLUS(mark(x0), a__plus(0, mark(x2))), MARK(plus(0, x2))) MARK(plus(x0, plus(s(z0), x2))) -> c8(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) MARK(plus(and(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(plus(z0, z1), plus(x1, x2))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(tt, plus(x1, x2))) -> c8(A__PLUS(tt, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(0, plus(x1, x2))) -> c8(A__PLUS(0, a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(s(z0), plus(x1, x2))) -> c8(A__PLUS(s(mark(z0)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) MARK(plus(x0, plus(x1, x2))) -> c8(MARK(plus(x1, x2))) MARK(plus(x0, s(and(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__and(mark(z0), z1))), MARK(s(and(z0, z1)))) MARK(plus(x0, s(plus(z0, z1)))) -> c8(A__PLUS(mark(x0), s(a__plus(mark(z0), mark(z1)))), MARK(s(plus(z0, z1)))) MARK(plus(x0, s(tt))) -> c8(A__PLUS(mark(x0), s(tt)), MARK(s(tt))) MARK(plus(x0, s(0))) -> c8(A__PLUS(mark(x0), s(0)), MARK(s(0))) MARK(plus(x0, s(s(z0)))) -> c8(A__PLUS(mark(x0), s(s(mark(z0)))), MARK(s(s(z0)))) MARK(plus(and(z0, z1), s(x1))) -> c8(A__PLUS(a__and(mark(z0), z1), s(mark(x1))), MARK(s(x1))) MARK(plus(plus(z0, z1), s(x1))) -> c8(A__PLUS(a__plus(mark(z0), mark(z1)), s(mark(x1))), MARK(s(x1))) MARK(plus(tt, s(x1))) -> c8(A__PLUS(tt, s(mark(x1))), MARK(s(x1))) MARK(plus(0, s(x1))) -> c8(A__PLUS(0, s(mark(x1))), MARK(s(x1))) MARK(plus(s(z0), s(x1))) -> c8(A__PLUS(s(mark(z0)), s(mark(x1))), MARK(s(x1))) MARK(plus(x0, s(x1))) -> c8(MARK(s(x1))) MARK(plus(and(x0, z1), x2)) -> c8(A__PLUS(and(mark(x0), z1), mark(x2)), MARK(x2)) MARK(plus(and(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__and(mark(z0), z1), x1), mark(x2)), MARK(x2)) MARK(plus(and(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), MARK(x2)) MARK(plus(and(tt, x1), x2)) -> c8(A__PLUS(a__and(tt, x1), mark(x2)), MARK(x2)) MARK(plus(and(0, x1), x2)) -> c8(A__PLUS(a__and(0, x1), mark(x2)), MARK(x2)) MARK(plus(and(s(z0), x1), x2)) -> c8(A__PLUS(a__and(s(mark(z0)), x1), mark(x2)), MARK(x2)) MARK(plus(and(x0, x1), 0)) -> c8(A__PLUS(a__and(mark(x0), x1), 0)) MARK(plus(plus(x0, x1), x2)) -> c8(A__PLUS(plus(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, and(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, plus(z0, z1)), x2)) -> c8(A__PLUS(a__plus(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(plus(plus(x0, tt), x2)) -> c8(A__PLUS(a__plus(mark(x0), tt), mark(x2)), MARK(x2)) MARK(plus(plus(x0, 0), x2)) -> c8(A__PLUS(a__plus(mark(x0), 0), mark(x2)), MARK(x2)) MARK(plus(plus(x0, s(z0)), x2)) -> c8(A__PLUS(a__plus(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(plus(plus(and(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(plus(z0, z1), x1), x2)) -> c8(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(tt, x1), x2)) -> c8(A__PLUS(a__plus(tt, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(0, x1), x2)) -> c8(A__PLUS(a__plus(0, mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(s(z0), x1), x2)) -> c8(A__PLUS(a__plus(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(plus(plus(x0, x1), 0)) -> c8(A__PLUS(a__plus(mark(x0), mark(x1)), 0)) MARK(plus(tt, 0)) -> c8(A__PLUS(tt, 0)) MARK(plus(0, 0)) -> c8(A__PLUS(0, 0)) MARK(plus(s(and(z0, z1)), x1)) -> c8(A__PLUS(s(a__and(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(plus(s(plus(z0, z1)), x1)) -> c8(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(plus(s(tt), x1)) -> c8(A__PLUS(s(tt), mark(x1)), MARK(x1)) MARK(plus(s(0), x1)) -> c8(A__PLUS(s(0), mark(x1)), MARK(x1)) MARK(plus(s(s(z0)), x1)) -> c8(A__PLUS(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(plus(s(x0), 0)) -> c8(A__PLUS(s(mark(x0)), 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1 Compound Symbols: c_1, c2_1, c11_1, c3_2, c3_1, c4_1, c6_1, c7_2, c7_1, c8_1, c4_2, c6_2, c8_2 ---------------------------------------- (237) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (238) 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__and(tt, X) -> mark(X) [1] a__plus(N, 0) -> mark(N) [1] a__plus(N, s(M)) -> s(a__plus(mark(N), mark(M))) [1] mark(and(X1, X2)) -> a__and(mark(X1), X2) [1] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(tt) -> tt [1] mark(0) -> 0 [1] mark(s(X)) -> s(mark(X)) [1] a__and(X1, X2) -> and(X1, X2) [1] a__plus(X1, X2) -> plus(X1, X2) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (239) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (240) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__and(tt, X) -> mark(X) [1] a__plus(N, 0) -> mark(N) [1] a__plus(N, s(M)) -> s(a__plus(mark(N), mark(M))) [1] mark(and(X1, X2)) -> a__and(mark(X1), X2) [1] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(tt) -> tt [1] mark(0) -> 0 [1] mark(s(X)) -> s(mark(X)) [1] a__and(X1, X2) -> and(X1, X2) [1] a__plus(X1, X2) -> plus(X1, X2) [1] The TRS has the following type information: a__and :: tt:0:s:and:plus -> tt:0:s:and:plus -> tt:0:s:and:plus tt :: tt:0:s:and:plus mark :: tt:0:s:and:plus -> tt:0:s:and:plus a__plus :: tt:0:s:and:plus -> tt:0:s:and:plus -> tt:0:s:and:plus 0 :: tt:0:s:and:plus s :: tt:0:s:and:plus -> tt:0:s:and:plus and :: tt:0:s:and:plus -> tt:0:s:and:plus -> tt:0:s:and:plus plus :: tt:0:s:and:plus -> tt:0:s:and:plus -> tt:0:s:and:plus Rewrite Strategy: INNERMOST ---------------------------------------- (241) 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 ---------------------------------------- (242) 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__and(tt, X) -> mark(X) [1] a__plus(N, 0) -> mark(N) [1] a__plus(N, s(M)) -> s(a__plus(mark(N), mark(M))) [1] mark(and(X1, X2)) -> a__and(mark(X1), X2) [1] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(tt) -> tt [1] mark(0) -> 0 [1] mark(s(X)) -> s(mark(X)) [1] a__and(X1, X2) -> and(X1, X2) [1] a__plus(X1, X2) -> plus(X1, X2) [1] The TRS has the following type information: a__and :: tt:0:s:and:plus -> tt:0:s:and:plus -> tt:0:s:and:plus tt :: tt:0:s:and:plus mark :: tt:0:s:and:plus -> tt:0:s:and:plus a__plus :: tt:0:s:and:plus -> tt:0:s:and:plus -> tt:0:s:and:plus 0 :: tt:0:s:and:plus s :: tt:0:s:and:plus -> tt:0:s:and:plus and :: tt:0:s:and:plus -> tt:0:s:and:plus -> tt:0:s:and:plus plus :: tt:0:s:and:plus -> tt:0:s:and:plus -> tt:0:s:and:plus Rewrite Strategy: INNERMOST ---------------------------------------- (243) 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 ---------------------------------------- (244) Obligation: Complexity RNTS consisting of the following rules: 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__plus(z, z') -{ 1 }-> mark(N) :|: z = N, z' = 0, N >= 0 a__plus(z, z') -{ 1 }-> 1 + a__plus(mark(N), mark(M)) :|: z' = 1 + M, z = N, M >= 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__and(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. ---------------------------------------- (245) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: none (c) The following functions are completely defined: mark_1 a__plus_2 a__and_2 Due to the following rules being added: none And the following fresh constants: none ---------------------------------------- (246) 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__and(tt, X) -> mark(X) [1] a__plus(N, 0) -> mark(N) [1] a__plus(N, s(M)) -> s(a__plus(mark(N), mark(M))) [1] mark(and(X1, X2)) -> a__and(mark(X1), X2) [1] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(tt) -> tt [1] mark(0) -> 0 [1] mark(s(X)) -> s(mark(X)) [1] a__and(X1, X2) -> and(X1, X2) [1] a__plus(X1, X2) -> plus(X1, X2) [1] The TRS has the following type information: a__and :: tt:0:s:and:plus -> tt:0:s:and:plus -> tt:0:s:and:plus tt :: tt:0:s:and:plus mark :: tt:0:s:and:plus -> tt:0:s:and:plus a__plus :: tt:0:s:and:plus -> tt:0:s:and:plus -> tt:0:s:and:plus 0 :: tt:0:s:and:plus s :: tt:0:s:and:plus -> tt:0:s:and:plus and :: tt:0:s:and:plus -> tt:0:s:and:plus -> tt:0:s:and:plus plus :: tt:0:s:and:plus -> tt:0:s:and:plus -> tt:0:s:and:plus Rewrite Strategy: INNERMOST ---------------------------------------- (247) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (248) 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__and(tt, X) -> mark(X) [1] a__plus(N, 0) -> mark(N) [1] a__plus(N, s(M)) -> s(a__plus(mark(N), mark(M))) [1] mark(and(and(X111, X211), X2)) -> a__and(a__and(mark(X111), X211), X2) [2] mark(and(plus(X112, X212), X2)) -> a__and(a__plus(mark(X112), mark(X212)), X2) [2] mark(and(tt, X2)) -> a__and(tt, X2) [2] mark(and(0, X2)) -> a__and(0, X2) [2] mark(and(s(X7), X2)) -> a__and(s(mark(X7)), X2) [2] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(tt) -> tt [1] mark(0) -> 0 [1] mark(s(X)) -> s(mark(X)) [1] a__and(X1, X2) -> and(X1, X2) [1] a__plus(X1, X2) -> plus(X1, X2) [1] The TRS has the following type information: a__and :: tt:0:s:and:plus -> tt:0:s:and:plus -> tt:0:s:and:plus tt :: tt:0:s:and:plus mark :: tt:0:s:and:plus -> tt:0:s:and:plus a__plus :: tt:0:s:and:plus -> tt:0:s:and:plus -> tt:0:s:and:plus 0 :: tt:0:s:and:plus s :: tt:0:s:and:plus -> tt:0:s:and:plus and :: tt:0:s:and:plus -> tt:0:s:and:plus -> tt:0:s:and:plus plus :: tt:0:s:and:plus -> tt:0:s:and:plus -> tt:0:s:and:plus Rewrite Strategy: INNERMOST ---------------------------------------- (249) 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 ---------------------------------------- (250) Obligation: Complexity RNTS consisting of the following rules: 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__plus(z, z') -{ 1 }-> mark(N) :|: z = N, z' = 0, N >= 0 a__plus(z, z') -{ 1 }-> 1 + a__plus(mark(N), mark(M)) :|: z' = 1 + M, z = N, M >= 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) -{ 2 }-> a__and(a__plus(mark(X112), mark(X212)), X2) :|: X212 >= 0, z = 1 + (1 + X112 + X212) + X2, X112 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__and(mark(X111), X211), X2) :|: z = 1 + (1 + X111 + X211) + X2, X211 >= 0, X2 >= 0, X111 >= 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(X7), X2) :|: z = 1 + (1 + X7) + X2, X7 >= 0, X2 >= 0 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 ---------------------------------------- (251) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (252) Obligation: Complexity RNTS consisting of the following rules: a__and(z, z') -{ 1 }-> mark(z') :|: z = 1, z' >= 0 a__and(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__plus(z, z') -{ 1 }-> mark(z) :|: z' = 0, z >= 0 a__plus(z, z') -{ 1 }-> 1 + a__plus(mark(z), mark(z' - 1)) :|: z' - 1 >= 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) -{ 2 }-> a__and(a__plus(mark(X112), mark(X212)), X2) :|: X212 >= 0, z = 1 + (1 + X112 + X212) + X2, X112 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__and(mark(X111), X211), X2) :|: z = 1 + (1 + X111 + X211) + X2, X211 >= 0, X2 >= 0, X111 >= 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(X7), X2) :|: z = 1 + (1 + X7) + X2, X7 >= 0, X2 >= 0 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(z - 1) :|: z - 1 >= 0