KILLED proof of input_eYnPgUS30z.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).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), 43 ms] (6) CdtProblem (7) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxRelTRS (9) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CpxRelTRS (11) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (12) typed CpxTrs (13) OrderProof [LOWER BOUND(ID), 0 ms] (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 679 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 843 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 325 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 66 ms] (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 535 ms] (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 487 ms] (26) BEST (27) proven lower bound (28) LowerBoundPropagationProof [FINISHED, 0 ms] (29) BOUNDS(n^1, INF) (30) typed CpxTrs (31) RewriteLemmaProof [LOWER BOUND(ID), 2120 ms] (32) typed CpxTrs (33) RewriteLemmaProof [LOWER BOUND(ID), 521 ms] (34) BOUNDS(1, INF) (35) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (36) CpxWeightedTrs (37) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (38) CpxTypedWeightedTrs (39) CompletionProof [UPPER BOUND(ID), 0 ms] (40) CpxTypedWeightedCompleteTrs (41) NarrowingProof [BOTH BOUNDS(ID, ID), 38 ms] (42) CpxTypedWeightedCompleteTrs (43) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (44) CpxRNTS (45) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CpxRNTS (47) CompletionProof [UPPER BOUND(ID), 0 ms] (48) CpxTypedWeightedCompleteTrs (49) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (50) CpxRNTS (51) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (52) CdtProblem (53) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CdtProblem (55) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CpxRelTRS (57) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (58) CpxTRS (59) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CpxWeightedTrs (61) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CpxTypedWeightedTrs (63) CompletionProof [UPPER BOUND(ID), 0 ms] (64) CpxTypedWeightedCompleteTrs (65) NarrowingProof [BOTH BOUNDS(ID, ID), 4690 ms] (66) CpxTypedWeightedCompleteTrs (67) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (68) CpxRNTS (69) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CpxRNTS (71) CompletionProof [UPPER BOUND(ID), 0 ms] (72) CpxTypedWeightedCompleteTrs (73) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (74) CpxRNTS (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3 ms] (80) CdtProblem (81) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 7 ms] (90) CdtProblem (91) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4 ms] (100) CdtProblem (101) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (106) CdtProblem (107) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem (111) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 18 ms] (116) CdtProblem (117) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 19 ms] (120) CdtProblem (121) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (122) CdtProblem (123) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (126) CdtProblem (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (128) CdtProblem (129) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 74 ms] (132) CdtProblem (133) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (134) CdtProblem (135) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 49 ms] (136) CdtProblem (137) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (138) CdtProblem (139) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 47 ms] (140) CdtProblem (141) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 81 ms] (144) CdtProblem (145) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (146) CdtProblem (147) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 17 ms] (148) CdtProblem (149) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (150) CdtProblem (151) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (152) CdtProblem (153) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (154) CdtProblem (155) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 8 ms] (156) CdtProblem (157) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (158) CdtProblem (159) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 44 ms] (160) CdtProblem (161) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (162) CdtProblem (163) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 76 ms] (164) CdtProblem (165) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (166) CdtProblem (167) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 124 ms] (168) CdtProblem (169) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 24 ms] (170) CdtProblem (171) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 92 ms] (172) CdtProblem (173) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (174) CdtProblem (175) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 34 ms] (176) CdtProblem (177) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 96 ms] (178) CdtProblem (179) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (180) CdtProblem (181) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (182) CdtProblem (183) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 168 ms] (184) CdtProblem (185) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 11 ms] (186) CdtProblem (187) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 25 ms] (188) CdtProblem (189) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 159 ms] (190) CdtProblem (191) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (192) CdtProblem (193) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 41 ms] (194) CdtProblem (195) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 48 ms] (196) CdtProblem (197) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (198) CdtProblem (199) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 34 ms] (200) CdtProblem (201) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 38 ms] (202) CdtProblem (203) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (204) CdtProblem (205) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 48 ms] (206) CdtProblem (207) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 54 ms] (208) CdtProblem (209) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 1 ms] (210) CdtProblem (211) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (212) CdtProblem (213) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 129 ms] (214) CdtProblem (215) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (216) CdtProblem (217) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 230 ms] (218) CdtProblem (219) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 37 ms] (220) CdtProblem (221) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 216 ms] (222) CdtProblem (223) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 26 ms] (224) CdtProblem (225) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 129 ms] (226) CdtProblem (227) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 177 ms] (228) CdtProblem (229) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 48 ms] (230) CdtProblem (231) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 191 ms] (232) CdtProblem (233) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 39 ms] (234) CdtProblem (235) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 334 ms] (236) CdtProblem (237) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 5 ms] (238) CdtProblem (239) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 440 ms] (240) CdtProblem (241) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 43 ms] (242) CdtProblem (243) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 205 ms] (244) CdtProblem (245) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 76 ms] (246) CdtProblem (247) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 263 ms] (248) CdtProblem (249) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 38 ms] (250) CdtProblem (251) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 287 ms] (252) CdtProblem (253) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 109 ms] (254) CdtProblem (255) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 366 ms] (256) CdtProblem (257) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 78 ms] (258) CdtProblem ---------------------------------------- (0) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__and(tt, X) -> mark(X) a__plus(N, 0) -> mark(N) a__plus(N, s(M)) -> s(a__plus(mark(N), mark(M))) a__x(N, 0) -> 0 a__x(N, s(M)) -> a__plus(a__x(mark(N), mark(M)), mark(N)) mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) mark(x(X1, X2)) -> a__x(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) a__x(X1, X2) -> x(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))) a__x(N, 0') -> 0' a__x(N, s(M)) -> a__plus(a__x(mark(N), mark(M)), mark(N)) mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) mark(x(X1, X2)) -> a__x(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) a__x(X1, X2) -> x(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))) a__x(N, 0) -> 0 a__x(N, s(M)) -> a__plus(a__x(mark(N), mark(M)), mark(N)) mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) mark(x(X1, X2)) -> a__x(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) a__x(X1, X2) -> x(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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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 A__X(z0, 0) -> c6 A__X(z0, s(z1)) -> c7(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z0)) A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) A__X(z0, z1) -> c10 MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c16 MARK(0) -> c17 MARK(s(z0)) -> c18(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 A__X(z0, 0) -> c6 A__X(z0, s(z1)) -> c7(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z0)) A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) A__X(z0, z1) -> c10 MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c16 MARK(0) -> c17 MARK(s(z0)) -> c18(MARK(z0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, A__X_2, MARK_1 Compound Symbols: c_1, c1, c2_1, c3_2, c4_2, c5, c6, c7_3, c8_3, c9_2, c10, c11_2, c12_2, c13_2, c14_2, c15_2, c16, c17, c18_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 A__X(z0, 0) -> c6 A__X(z0, s(z1)) -> c7(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z0)) A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) A__X(z0, z1) -> c10 MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c16 MARK(0) -> c17 MARK(s(z0)) -> c18(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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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 A__X(z0, 0') -> c6 A__X(z0, s(z1)) -> c7(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z0)) A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) A__X(z0, z1) -> c10 MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c16 MARK(0') -> c17 MARK(s(z0)) -> c18(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) a__x(z0, 0') -> 0' a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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 A__X(z0, 0') -> c6 A__X(z0, s(z1)) -> c7(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z0)) A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) A__X(z0, z1) -> c10 MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c16 MARK(0') -> c17 MARK(s(z0)) -> c18(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) a__x(z0, 0') -> 0' a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(0') -> 0' mark(s(z0)) -> s(mark(z0)) Types: A__AND :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> c:c1 tt :: tt:0':s:and:plus:x c :: c11:c12:c13:c14:c15:c16:c17:c18 -> c:c1 MARK :: tt:0':s:and:plus:x -> c11:c12:c13:c14:c15:c16:c17:c18 c1 :: c:c1 A__PLUS :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> c2:c3:c4:c5 0' :: tt:0':s:and:plus:x c2 :: c11:c12:c13:c14:c15:c16:c17:c18 -> c2:c3:c4:c5 s :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x c3 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c2:c3:c4:c5 mark :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x c4 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c2:c3:c4:c5 c5 :: c2:c3:c4:c5 A__X :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> c6:c7:c8:c9:c10 c6 :: c6:c7:c8:c9:c10 c7 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c6:c7:c8:c9:c10 a__x :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c8 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c6:c7:c8:c9:c10 c9 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c6:c7:c8:c9:c10 c10 :: c6:c7:c8:c9:c10 and :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c11 :: c:c1 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 plus :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c12 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 c13 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 x :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c14 :: c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 c15 :: c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 c16 :: c11:c12:c13:c14:c15:c16:c17:c18 c17 :: c11:c12:c13:c14:c15:c16:c17:c18 c18 :: c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 a__and :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x a__plus :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x hole_c:c11_19 :: c:c1 hole_tt:0':s:and:plus:x2_19 :: tt:0':s:and:plus:x hole_c11:c12:c13:c14:c15:c16:c17:c183_19 :: c11:c12:c13:c14:c15:c16:c17:c18 hole_c2:c3:c4:c54_19 :: c2:c3:c4:c5 hole_c6:c7:c8:c9:c105_19 :: c6:c7:c8:c9:c10 gen_tt:0':s:and:plus:x6_19 :: Nat -> tt:0':s:and:plus:x gen_c11:c12:c13:c14:c15:c16:c17:c187_19 :: Nat -> c11:c12:c13:c14:c15:c16:c17:c18 gen_c2:c3:c4:c58_19 :: Nat -> c2:c3:c4:c5 gen_c6:c7:c8:c9:c109_19 :: Nat -> c6:c7:c8:c9:c10 ---------------------------------------- (13) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: MARK, A__PLUS, mark, A__X, a__x, a__plus They will be analysed ascendingly in the following order: MARK = A__PLUS mark < MARK MARK = A__X mark < A__PLUS A__PLUS = A__X mark < A__X mark = a__x mark = a__plus a__x < A__X a__x = 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 A__X(z0, 0') -> c6 A__X(z0, s(z1)) -> c7(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z0)) A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) A__X(z0, z1) -> c10 MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c16 MARK(0') -> c17 MARK(s(z0)) -> c18(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) a__x(z0, 0') -> 0' a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(0') -> 0' mark(s(z0)) -> s(mark(z0)) Types: A__AND :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> c:c1 tt :: tt:0':s:and:plus:x c :: c11:c12:c13:c14:c15:c16:c17:c18 -> c:c1 MARK :: tt:0':s:and:plus:x -> c11:c12:c13:c14:c15:c16:c17:c18 c1 :: c:c1 A__PLUS :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> c2:c3:c4:c5 0' :: tt:0':s:and:plus:x c2 :: c11:c12:c13:c14:c15:c16:c17:c18 -> c2:c3:c4:c5 s :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x c3 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c2:c3:c4:c5 mark :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x c4 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c2:c3:c4:c5 c5 :: c2:c3:c4:c5 A__X :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> c6:c7:c8:c9:c10 c6 :: c6:c7:c8:c9:c10 c7 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c6:c7:c8:c9:c10 a__x :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c8 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c6:c7:c8:c9:c10 c9 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c6:c7:c8:c9:c10 c10 :: c6:c7:c8:c9:c10 and :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c11 :: c:c1 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 plus :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c12 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 c13 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 x :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c14 :: c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 c15 :: c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 c16 :: c11:c12:c13:c14:c15:c16:c17:c18 c17 :: c11:c12:c13:c14:c15:c16:c17:c18 c18 :: c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 a__and :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x a__plus :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x hole_c:c11_19 :: c:c1 hole_tt:0':s:and:plus:x2_19 :: tt:0':s:and:plus:x hole_c11:c12:c13:c14:c15:c16:c17:c183_19 :: c11:c12:c13:c14:c15:c16:c17:c18 hole_c2:c3:c4:c54_19 :: c2:c3:c4:c5 hole_c6:c7:c8:c9:c105_19 :: c6:c7:c8:c9:c10 gen_tt:0':s:and:plus:x6_19 :: Nat -> tt:0':s:and:plus:x gen_c11:c12:c13:c14:c15:c16:c17:c187_19 :: Nat -> c11:c12:c13:c14:c15:c16:c17:c18 gen_c2:c3:c4:c58_19 :: Nat -> c2:c3:c4:c5 gen_c6:c7:c8:c9:c109_19 :: Nat -> c6:c7:c8:c9:c10 Generator Equations: gen_tt:0':s:and:plus:x6_19(0) <=> tt gen_tt:0':s:and:plus:x6_19(+(x, 1)) <=> s(gen_tt:0':s:and:plus:x6_19(x)) gen_c11:c12:c13:c14:c15:c16:c17:c187_19(0) <=> c16 gen_c11:c12:c13:c14:c15:c16:c17:c187_19(+(x, 1)) <=> c11(c(c16), gen_c11:c12:c13:c14:c15:c16:c17:c187_19(x)) gen_c2:c3:c4:c58_19(0) <=> c2(c16) gen_c2:c3:c4:c58_19(+(x, 1)) <=> c3(gen_c2:c3:c4:c58_19(x), c16) gen_c6:c7:c8:c9:c109_19(0) <=> c6 gen_c6:c7:c8:c9:c109_19(+(x, 1)) <=> c7(c2(c16), gen_c6:c7:c8:c9:c109_19(x), c16) The following defined symbols remain to be analysed: a__plus, MARK, A__PLUS, mark, A__X, a__x They will be analysed ascendingly in the following order: MARK = A__PLUS mark < MARK MARK = A__X mark < A__PLUS A__PLUS = A__X mark < A__X mark = a__x mark = a__plus a__x < A__X a__x = a__plus ---------------------------------------- (15) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: mark(gen_tt:0':s:and:plus:x6_19(n12198_19)) -> gen_tt:0':s:and:plus:x6_19(n12198_19), rt in Omega(0) Induction Base: mark(gen_tt:0':s:and:plus:x6_19(0)) ->_R^Omega(0) tt Induction Step: mark(gen_tt:0':s:and:plus:x6_19(+(n12198_19, 1))) ->_R^Omega(0) s(mark(gen_tt:0':s:and:plus:x6_19(n12198_19))) ->_IH s(gen_tt:0':s:and:plus:x6_19(c12199_19)) 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 A__X(z0, 0') -> c6 A__X(z0, s(z1)) -> c7(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z0)) A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) A__X(z0, z1) -> c10 MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c16 MARK(0') -> c17 MARK(s(z0)) -> c18(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) a__x(z0, 0') -> 0' a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(0') -> 0' mark(s(z0)) -> s(mark(z0)) Types: A__AND :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> c:c1 tt :: tt:0':s:and:plus:x c :: c11:c12:c13:c14:c15:c16:c17:c18 -> c:c1 MARK :: tt:0':s:and:plus:x -> c11:c12:c13:c14:c15:c16:c17:c18 c1 :: c:c1 A__PLUS :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> c2:c3:c4:c5 0' :: tt:0':s:and:plus:x c2 :: c11:c12:c13:c14:c15:c16:c17:c18 -> c2:c3:c4:c5 s :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x c3 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c2:c3:c4:c5 mark :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x c4 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c2:c3:c4:c5 c5 :: c2:c3:c4:c5 A__X :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> c6:c7:c8:c9:c10 c6 :: c6:c7:c8:c9:c10 c7 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c6:c7:c8:c9:c10 a__x :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c8 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c6:c7:c8:c9:c10 c9 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c6:c7:c8:c9:c10 c10 :: c6:c7:c8:c9:c10 and :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c11 :: c:c1 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 plus :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c12 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 c13 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 x :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c14 :: c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 c15 :: c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 c16 :: c11:c12:c13:c14:c15:c16:c17:c18 c17 :: c11:c12:c13:c14:c15:c16:c17:c18 c18 :: c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 a__and :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x a__plus :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x hole_c:c11_19 :: c:c1 hole_tt:0':s:and:plus:x2_19 :: tt:0':s:and:plus:x hole_c11:c12:c13:c14:c15:c16:c17:c183_19 :: c11:c12:c13:c14:c15:c16:c17:c18 hole_c2:c3:c4:c54_19 :: c2:c3:c4:c5 hole_c6:c7:c8:c9:c105_19 :: c6:c7:c8:c9:c10 gen_tt:0':s:and:plus:x6_19 :: Nat -> tt:0':s:and:plus:x gen_c11:c12:c13:c14:c15:c16:c17:c187_19 :: Nat -> c11:c12:c13:c14:c15:c16:c17:c18 gen_c2:c3:c4:c58_19 :: Nat -> c2:c3:c4:c5 gen_c6:c7:c8:c9:c109_19 :: Nat -> c6:c7:c8:c9:c10 Lemmas: mark(gen_tt:0':s:and:plus:x6_19(n12198_19)) -> gen_tt:0':s:and:plus:x6_19(n12198_19), rt in Omega(0) Generator Equations: gen_tt:0':s:and:plus:x6_19(0) <=> tt gen_tt:0':s:and:plus:x6_19(+(x, 1)) <=> s(gen_tt:0':s:and:plus:x6_19(x)) gen_c11:c12:c13:c14:c15:c16:c17:c187_19(0) <=> c16 gen_c11:c12:c13:c14:c15:c16:c17:c187_19(+(x, 1)) <=> c11(c(c16), gen_c11:c12:c13:c14:c15:c16:c17:c187_19(x)) gen_c2:c3:c4:c58_19(0) <=> c2(c16) gen_c2:c3:c4:c58_19(+(x, 1)) <=> c3(gen_c2:c3:c4:c58_19(x), c16) gen_c6:c7:c8:c9:c109_19(0) <=> c6 gen_c6:c7:c8:c9:c109_19(+(x, 1)) <=> c7(c2(c16), gen_c6:c7:c8:c9:c109_19(x), c16) The following defined symbols remain to be analysed: a__x, MARK, A__PLUS, A__X, a__plus They will be analysed ascendingly in the following order: MARK = A__PLUS mark < MARK MARK = A__X mark < A__PLUS A__PLUS = A__X mark < A__X mark = a__x mark = a__plus a__x < A__X a__x = a__plus ---------------------------------------- (17) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: a__x(gen_tt:0':s:and:plus:x6_19(a), gen_tt:0':s:and:plus:x6_19(+(1, n13459_19))) -> *10_19, rt in Omega(0) Induction Base: a__x(gen_tt:0':s:and:plus:x6_19(a), gen_tt:0':s:and:plus:x6_19(+(1, 0))) Induction Step: a__x(gen_tt:0':s:and:plus:x6_19(a), gen_tt:0':s:and:plus:x6_19(+(1, +(n13459_19, 1)))) ->_R^Omega(0) a__plus(a__x(mark(gen_tt:0':s:and:plus:x6_19(a)), mark(gen_tt:0':s:and:plus:x6_19(+(1, n13459_19)))), mark(gen_tt:0':s:and:plus:x6_19(a))) ->_L^Omega(0) a__plus(a__x(gen_tt:0':s:and:plus:x6_19(a), mark(gen_tt:0':s:and:plus:x6_19(+(1, n13459_19)))), mark(gen_tt:0':s:and:plus:x6_19(a))) ->_L^Omega(0) a__plus(a__x(gen_tt:0':s:and:plus:x6_19(a), gen_tt:0':s:and:plus:x6_19(+(1, n13459_19))), mark(gen_tt:0':s:and:plus:x6_19(a))) ->_IH a__plus(*10_19, mark(gen_tt:0':s:and:plus:x6_19(a))) ->_L^Omega(0) a__plus(*10_19, gen_tt:0':s:and:plus:x6_19(a)) 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 A__X(z0, 0') -> c6 A__X(z0, s(z1)) -> c7(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z0)) A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) A__X(z0, z1) -> c10 MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c16 MARK(0') -> c17 MARK(s(z0)) -> c18(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) a__x(z0, 0') -> 0' a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(0') -> 0' mark(s(z0)) -> s(mark(z0)) Types: A__AND :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> c:c1 tt :: tt:0':s:and:plus:x c :: c11:c12:c13:c14:c15:c16:c17:c18 -> c:c1 MARK :: tt:0':s:and:plus:x -> c11:c12:c13:c14:c15:c16:c17:c18 c1 :: c:c1 A__PLUS :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> c2:c3:c4:c5 0' :: tt:0':s:and:plus:x c2 :: c11:c12:c13:c14:c15:c16:c17:c18 -> c2:c3:c4:c5 s :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x c3 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c2:c3:c4:c5 mark :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x c4 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c2:c3:c4:c5 c5 :: c2:c3:c4:c5 A__X :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> c6:c7:c8:c9:c10 c6 :: c6:c7:c8:c9:c10 c7 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c6:c7:c8:c9:c10 a__x :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c8 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c6:c7:c8:c9:c10 c9 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c6:c7:c8:c9:c10 c10 :: c6:c7:c8:c9:c10 and :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c11 :: c:c1 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 plus :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c12 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 c13 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 x :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c14 :: c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 c15 :: c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 c16 :: c11:c12:c13:c14:c15:c16:c17:c18 c17 :: c11:c12:c13:c14:c15:c16:c17:c18 c18 :: c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 a__and :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x a__plus :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x hole_c:c11_19 :: c:c1 hole_tt:0':s:and:plus:x2_19 :: tt:0':s:and:plus:x hole_c11:c12:c13:c14:c15:c16:c17:c183_19 :: c11:c12:c13:c14:c15:c16:c17:c18 hole_c2:c3:c4:c54_19 :: c2:c3:c4:c5 hole_c6:c7:c8:c9:c105_19 :: c6:c7:c8:c9:c10 gen_tt:0':s:and:plus:x6_19 :: Nat -> tt:0':s:and:plus:x gen_c11:c12:c13:c14:c15:c16:c17:c187_19 :: Nat -> c11:c12:c13:c14:c15:c16:c17:c18 gen_c2:c3:c4:c58_19 :: Nat -> c2:c3:c4:c5 gen_c6:c7:c8:c9:c109_19 :: Nat -> c6:c7:c8:c9:c10 Lemmas: mark(gen_tt:0':s:and:plus:x6_19(n12198_19)) -> gen_tt:0':s:and:plus:x6_19(n12198_19), rt in Omega(0) a__x(gen_tt:0':s:and:plus:x6_19(a), gen_tt:0':s:and:plus:x6_19(+(1, n13459_19))) -> *10_19, rt in Omega(0) Generator Equations: gen_tt:0':s:and:plus:x6_19(0) <=> tt gen_tt:0':s:and:plus:x6_19(+(x, 1)) <=> s(gen_tt:0':s:and:plus:x6_19(x)) gen_c11:c12:c13:c14:c15:c16:c17:c187_19(0) <=> c16 gen_c11:c12:c13:c14:c15:c16:c17:c187_19(+(x, 1)) <=> c11(c(c16), gen_c11:c12:c13:c14:c15:c16:c17:c187_19(x)) gen_c2:c3:c4:c58_19(0) <=> c2(c16) gen_c2:c3:c4:c58_19(+(x, 1)) <=> c3(gen_c2:c3:c4:c58_19(x), c16) gen_c6:c7:c8:c9:c109_19(0) <=> c6 gen_c6:c7:c8:c9:c109_19(+(x, 1)) <=> c7(c2(c16), gen_c6:c7:c8:c9:c109_19(x), c16) The following defined symbols remain to be analysed: a__plus, MARK, A__PLUS, mark, A__X They will be analysed ascendingly in the following order: MARK = A__PLUS mark < MARK MARK = A__X mark < A__PLUS A__PLUS = A__X mark < A__X mark = a__x mark = a__plus a__x < A__X a__x = a__plus ---------------------------------------- (19) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: a__plus(gen_tt:0':s:and:plus:x6_19(a), gen_tt:0':s:and:plus:x6_19(+(1, n21738_19))) -> *10_19, rt in Omega(0) Induction Base: a__plus(gen_tt:0':s:and:plus:x6_19(a), gen_tt:0':s:and:plus:x6_19(+(1, 0))) Induction Step: a__plus(gen_tt:0':s:and:plus:x6_19(a), gen_tt:0':s:and:plus:x6_19(+(1, +(n21738_19, 1)))) ->_R^Omega(0) s(a__plus(mark(gen_tt:0':s:and:plus:x6_19(a)), mark(gen_tt:0':s:and:plus:x6_19(+(1, n21738_19))))) ->_L^Omega(0) s(a__plus(gen_tt:0':s:and:plus:x6_19(a), mark(gen_tt:0':s:and:plus:x6_19(+(1, n21738_19))))) ->_L^Omega(0) s(a__plus(gen_tt:0':s:and:plus:x6_19(a), gen_tt:0':s:and:plus:x6_19(+(1, n21738_19)))) ->_IH s(*10_19) 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 A__X(z0, 0') -> c6 A__X(z0, s(z1)) -> c7(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z0)) A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) A__X(z0, z1) -> c10 MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c16 MARK(0') -> c17 MARK(s(z0)) -> c18(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) a__x(z0, 0') -> 0' a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(0') -> 0' mark(s(z0)) -> s(mark(z0)) Types: A__AND :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> c:c1 tt :: tt:0':s:and:plus:x c :: c11:c12:c13:c14:c15:c16:c17:c18 -> c:c1 MARK :: tt:0':s:and:plus:x -> c11:c12:c13:c14:c15:c16:c17:c18 c1 :: c:c1 A__PLUS :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> c2:c3:c4:c5 0' :: tt:0':s:and:plus:x c2 :: c11:c12:c13:c14:c15:c16:c17:c18 -> c2:c3:c4:c5 s :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x c3 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c2:c3:c4:c5 mark :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x c4 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c2:c3:c4:c5 c5 :: c2:c3:c4:c5 A__X :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> c6:c7:c8:c9:c10 c6 :: c6:c7:c8:c9:c10 c7 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c6:c7:c8:c9:c10 a__x :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c8 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c6:c7:c8:c9:c10 c9 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c6:c7:c8:c9:c10 c10 :: c6:c7:c8:c9:c10 and :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c11 :: c:c1 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 plus :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c12 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 c13 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 x :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c14 :: c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 c15 :: c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 c16 :: c11:c12:c13:c14:c15:c16:c17:c18 c17 :: c11:c12:c13:c14:c15:c16:c17:c18 c18 :: c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 a__and :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x a__plus :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x hole_c:c11_19 :: c:c1 hole_tt:0':s:and:plus:x2_19 :: tt:0':s:and:plus:x hole_c11:c12:c13:c14:c15:c16:c17:c183_19 :: c11:c12:c13:c14:c15:c16:c17:c18 hole_c2:c3:c4:c54_19 :: c2:c3:c4:c5 hole_c6:c7:c8:c9:c105_19 :: c6:c7:c8:c9:c10 gen_tt:0':s:and:plus:x6_19 :: Nat -> tt:0':s:and:plus:x gen_c11:c12:c13:c14:c15:c16:c17:c187_19 :: Nat -> c11:c12:c13:c14:c15:c16:c17:c18 gen_c2:c3:c4:c58_19 :: Nat -> c2:c3:c4:c5 gen_c6:c7:c8:c9:c109_19 :: Nat -> c6:c7:c8:c9:c10 Lemmas: mark(gen_tt:0':s:and:plus:x6_19(n12198_19)) -> gen_tt:0':s:and:plus:x6_19(n12198_19), rt in Omega(0) a__x(gen_tt:0':s:and:plus:x6_19(a), gen_tt:0':s:and:plus:x6_19(+(1, n13459_19))) -> *10_19, rt in Omega(0) a__plus(gen_tt:0':s:and:plus:x6_19(a), gen_tt:0':s:and:plus:x6_19(+(1, n21738_19))) -> *10_19, rt in Omega(0) Generator Equations: gen_tt:0':s:and:plus:x6_19(0) <=> tt gen_tt:0':s:and:plus:x6_19(+(x, 1)) <=> s(gen_tt:0':s:and:plus:x6_19(x)) gen_c11:c12:c13:c14:c15:c16:c17:c187_19(0) <=> c16 gen_c11:c12:c13:c14:c15:c16:c17:c187_19(+(x, 1)) <=> c11(c(c16), gen_c11:c12:c13:c14:c15:c16:c17:c187_19(x)) gen_c2:c3:c4:c58_19(0) <=> c2(c16) gen_c2:c3:c4:c58_19(+(x, 1)) <=> c3(gen_c2:c3:c4:c58_19(x), c16) gen_c6:c7:c8:c9:c109_19(0) <=> c6 gen_c6:c7:c8:c9:c109_19(+(x, 1)) <=> c7(c2(c16), gen_c6:c7:c8:c9:c109_19(x), c16) The following defined symbols remain to be analysed: mark, MARK, A__PLUS, A__X, a__x They will be analysed ascendingly in the following order: MARK = A__PLUS mark < MARK MARK = A__X mark < A__PLUS A__PLUS = A__X mark < A__X mark = a__x mark = a__plus a__x < A__X a__x = a__plus ---------------------------------------- (21) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: mark(gen_tt:0':s:and:plus:x6_19(n25340_19)) -> gen_tt:0':s:and:plus:x6_19(n25340_19), rt in Omega(0) Induction Base: mark(gen_tt:0':s:and:plus:x6_19(0)) ->_R^Omega(0) tt Induction Step: mark(gen_tt:0':s:and:plus:x6_19(+(n25340_19, 1))) ->_R^Omega(0) s(mark(gen_tt:0':s:and:plus:x6_19(n25340_19))) ->_IH s(gen_tt:0':s:and:plus:x6_19(c25341_19)) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (22) 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 A__X(z0, 0') -> c6 A__X(z0, s(z1)) -> c7(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z0)) A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) A__X(z0, z1) -> c10 MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c16 MARK(0') -> c17 MARK(s(z0)) -> c18(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) a__x(z0, 0') -> 0' a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(0') -> 0' mark(s(z0)) -> s(mark(z0)) Types: A__AND :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> c:c1 tt :: tt:0':s:and:plus:x c :: c11:c12:c13:c14:c15:c16:c17:c18 -> c:c1 MARK :: tt:0':s:and:plus:x -> c11:c12:c13:c14:c15:c16:c17:c18 c1 :: c:c1 A__PLUS :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> c2:c3:c4:c5 0' :: tt:0':s:and:plus:x c2 :: c11:c12:c13:c14:c15:c16:c17:c18 -> c2:c3:c4:c5 s :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x c3 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c2:c3:c4:c5 mark :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x c4 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c2:c3:c4:c5 c5 :: c2:c3:c4:c5 A__X :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> c6:c7:c8:c9:c10 c6 :: c6:c7:c8:c9:c10 c7 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c6:c7:c8:c9:c10 a__x :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c8 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c6:c7:c8:c9:c10 c9 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c6:c7:c8:c9:c10 c10 :: c6:c7:c8:c9:c10 and :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c11 :: c:c1 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 plus :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c12 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 c13 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 x :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c14 :: c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 c15 :: c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 c16 :: c11:c12:c13:c14:c15:c16:c17:c18 c17 :: c11:c12:c13:c14:c15:c16:c17:c18 c18 :: c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 a__and :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x a__plus :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x hole_c:c11_19 :: c:c1 hole_tt:0':s:and:plus:x2_19 :: tt:0':s:and:plus:x hole_c11:c12:c13:c14:c15:c16:c17:c183_19 :: c11:c12:c13:c14:c15:c16:c17:c18 hole_c2:c3:c4:c54_19 :: c2:c3:c4:c5 hole_c6:c7:c8:c9:c105_19 :: c6:c7:c8:c9:c10 gen_tt:0':s:and:plus:x6_19 :: Nat -> tt:0':s:and:plus:x gen_c11:c12:c13:c14:c15:c16:c17:c187_19 :: Nat -> c11:c12:c13:c14:c15:c16:c17:c18 gen_c2:c3:c4:c58_19 :: Nat -> c2:c3:c4:c5 gen_c6:c7:c8:c9:c109_19 :: Nat -> c6:c7:c8:c9:c10 Lemmas: mark(gen_tt:0':s:and:plus:x6_19(n25340_19)) -> gen_tt:0':s:and:plus:x6_19(n25340_19), rt in Omega(0) a__x(gen_tt:0':s:and:plus:x6_19(a), gen_tt:0':s:and:plus:x6_19(+(1, n13459_19))) -> *10_19, rt in Omega(0) a__plus(gen_tt:0':s:and:plus:x6_19(a), gen_tt:0':s:and:plus:x6_19(+(1, n21738_19))) -> *10_19, rt in Omega(0) Generator Equations: gen_tt:0':s:and:plus:x6_19(0) <=> tt gen_tt:0':s:and:plus:x6_19(+(x, 1)) <=> s(gen_tt:0':s:and:plus:x6_19(x)) gen_c11:c12:c13:c14:c15:c16:c17:c187_19(0) <=> c16 gen_c11:c12:c13:c14:c15:c16:c17:c187_19(+(x, 1)) <=> c11(c(c16), gen_c11:c12:c13:c14:c15:c16:c17:c187_19(x)) gen_c2:c3:c4:c58_19(0) <=> c2(c16) gen_c2:c3:c4:c58_19(+(x, 1)) <=> c3(gen_c2:c3:c4:c58_19(x), c16) gen_c6:c7:c8:c9:c109_19(0) <=> c6 gen_c6:c7:c8:c9:c109_19(+(x, 1)) <=> c7(c2(c16), gen_c6:c7:c8:c9:c109_19(x), c16) The following defined symbols remain to be analysed: a__x, MARK, A__PLUS, A__X They will be analysed ascendingly in the following order: MARK = A__PLUS mark < MARK MARK = A__X mark < A__PLUS A__PLUS = A__X mark < A__X mark = a__x mark = a__plus a__x < A__X a__x = a__plus ---------------------------------------- (23) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: a__x(gen_tt:0':s:and:plus:x6_19(a), gen_tt:0':s:and:plus:x6_19(+(1, n26807_19))) -> *10_19, rt in Omega(0) Induction Base: a__x(gen_tt:0':s:and:plus:x6_19(a), gen_tt:0':s:and:plus:x6_19(+(1, 0))) Induction Step: a__x(gen_tt:0':s:and:plus:x6_19(a), gen_tt:0':s:and:plus:x6_19(+(1, +(n26807_19, 1)))) ->_R^Omega(0) a__plus(a__x(mark(gen_tt:0':s:and:plus:x6_19(a)), mark(gen_tt:0':s:and:plus:x6_19(+(1, n26807_19)))), mark(gen_tt:0':s:and:plus:x6_19(a))) ->_L^Omega(0) a__plus(a__x(gen_tt:0':s:and:plus:x6_19(a), mark(gen_tt:0':s:and:plus:x6_19(+(1, n26807_19)))), mark(gen_tt:0':s:and:plus:x6_19(a))) ->_L^Omega(0) a__plus(a__x(gen_tt:0':s:and:plus:x6_19(a), gen_tt:0':s:and:plus:x6_19(+(1, n26807_19))), mark(gen_tt:0':s:and:plus:x6_19(a))) ->_IH a__plus(*10_19, mark(gen_tt:0':s:and:plus:x6_19(a))) ->_L^Omega(0) a__plus(*10_19, gen_tt:0':s:and:plus:x6_19(a)) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (24) 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 A__X(z0, 0') -> c6 A__X(z0, s(z1)) -> c7(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z0)) A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) A__X(z0, z1) -> c10 MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c16 MARK(0') -> c17 MARK(s(z0)) -> c18(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) a__x(z0, 0') -> 0' a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(0') -> 0' mark(s(z0)) -> s(mark(z0)) Types: A__AND :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> c:c1 tt :: tt:0':s:and:plus:x c :: c11:c12:c13:c14:c15:c16:c17:c18 -> c:c1 MARK :: tt:0':s:and:plus:x -> c11:c12:c13:c14:c15:c16:c17:c18 c1 :: c:c1 A__PLUS :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> c2:c3:c4:c5 0' :: tt:0':s:and:plus:x c2 :: c11:c12:c13:c14:c15:c16:c17:c18 -> c2:c3:c4:c5 s :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x c3 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c2:c3:c4:c5 mark :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x c4 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c2:c3:c4:c5 c5 :: c2:c3:c4:c5 A__X :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> c6:c7:c8:c9:c10 c6 :: c6:c7:c8:c9:c10 c7 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c6:c7:c8:c9:c10 a__x :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c8 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c6:c7:c8:c9:c10 c9 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c6:c7:c8:c9:c10 c10 :: c6:c7:c8:c9:c10 and :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c11 :: c:c1 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 plus :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c12 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 c13 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 x :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c14 :: c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 c15 :: c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 c16 :: c11:c12:c13:c14:c15:c16:c17:c18 c17 :: c11:c12:c13:c14:c15:c16:c17:c18 c18 :: c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 a__and :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x a__plus :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x hole_c:c11_19 :: c:c1 hole_tt:0':s:and:plus:x2_19 :: tt:0':s:and:plus:x hole_c11:c12:c13:c14:c15:c16:c17:c183_19 :: c11:c12:c13:c14:c15:c16:c17:c18 hole_c2:c3:c4:c54_19 :: c2:c3:c4:c5 hole_c6:c7:c8:c9:c105_19 :: c6:c7:c8:c9:c10 gen_tt:0':s:and:plus:x6_19 :: Nat -> tt:0':s:and:plus:x gen_c11:c12:c13:c14:c15:c16:c17:c187_19 :: Nat -> c11:c12:c13:c14:c15:c16:c17:c18 gen_c2:c3:c4:c58_19 :: Nat -> c2:c3:c4:c5 gen_c6:c7:c8:c9:c109_19 :: Nat -> c6:c7:c8:c9:c10 Lemmas: mark(gen_tt:0':s:and:plus:x6_19(n25340_19)) -> gen_tt:0':s:and:plus:x6_19(n25340_19), rt in Omega(0) a__x(gen_tt:0':s:and:plus:x6_19(a), gen_tt:0':s:and:plus:x6_19(+(1, n26807_19))) -> *10_19, rt in Omega(0) a__plus(gen_tt:0':s:and:plus:x6_19(a), gen_tt:0':s:and:plus:x6_19(+(1, n21738_19))) -> *10_19, rt in Omega(0) Generator Equations: gen_tt:0':s:and:plus:x6_19(0) <=> tt gen_tt:0':s:and:plus:x6_19(+(x, 1)) <=> s(gen_tt:0':s:and:plus:x6_19(x)) gen_c11:c12:c13:c14:c15:c16:c17:c187_19(0) <=> c16 gen_c11:c12:c13:c14:c15:c16:c17:c187_19(+(x, 1)) <=> c11(c(c16), gen_c11:c12:c13:c14:c15:c16:c17:c187_19(x)) gen_c2:c3:c4:c58_19(0) <=> c2(c16) gen_c2:c3:c4:c58_19(+(x, 1)) <=> c3(gen_c2:c3:c4:c58_19(x), c16) gen_c6:c7:c8:c9:c109_19(0) <=> c6 gen_c6:c7:c8:c9:c109_19(+(x, 1)) <=> c7(c2(c16), gen_c6:c7:c8:c9:c109_19(x), c16) The following defined symbols remain to be analysed: A__PLUS, MARK, A__X They will be analysed ascendingly in the following order: MARK = A__PLUS MARK = A__X A__PLUS = A__X ---------------------------------------- (25) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: A__PLUS(gen_tt:0':s:and:plus:x6_19(a), gen_tt:0':s:and:plus:x6_19(+(1, n35904_19))) -> *10_19, rt in Omega(n35904_19) Induction Base: A__PLUS(gen_tt:0':s:and:plus:x6_19(a), gen_tt:0':s:and:plus:x6_19(+(1, 0))) Induction Step: A__PLUS(gen_tt:0':s:and:plus:x6_19(a), gen_tt:0':s:and:plus:x6_19(+(1, +(n35904_19, 1)))) ->_R^Omega(1) c3(A__PLUS(mark(gen_tt:0':s:and:plus:x6_19(a)), mark(gen_tt:0':s:and:plus:x6_19(+(1, n35904_19)))), MARK(gen_tt:0':s:and:plus:x6_19(a))) ->_L^Omega(0) c3(A__PLUS(gen_tt:0':s:and:plus:x6_19(a), mark(gen_tt:0':s:and:plus:x6_19(+(1, n35904_19)))), MARK(gen_tt:0':s:and:plus:x6_19(a))) ->_L^Omega(0) c3(A__PLUS(gen_tt:0':s:and:plus:x6_19(a), gen_tt:0':s:and:plus:x6_19(+(1, n35904_19))), MARK(gen_tt:0':s:and:plus:x6_19(a))) ->_IH c3(*10_19, MARK(gen_tt:0':s:and:plus:x6_19(a))) We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (26) Complex Obligation (BEST) ---------------------------------------- (27) 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 A__X(z0, 0') -> c6 A__X(z0, s(z1)) -> c7(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z0)) A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) A__X(z0, z1) -> c10 MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c16 MARK(0') -> c17 MARK(s(z0)) -> c18(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) a__x(z0, 0') -> 0' a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(0') -> 0' mark(s(z0)) -> s(mark(z0)) Types: A__AND :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> c:c1 tt :: tt:0':s:and:plus:x c :: c11:c12:c13:c14:c15:c16:c17:c18 -> c:c1 MARK :: tt:0':s:and:plus:x -> c11:c12:c13:c14:c15:c16:c17:c18 c1 :: c:c1 A__PLUS :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> c2:c3:c4:c5 0' :: tt:0':s:and:plus:x c2 :: c11:c12:c13:c14:c15:c16:c17:c18 -> c2:c3:c4:c5 s :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x c3 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c2:c3:c4:c5 mark :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x c4 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c2:c3:c4:c5 c5 :: c2:c3:c4:c5 A__X :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> c6:c7:c8:c9:c10 c6 :: c6:c7:c8:c9:c10 c7 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c6:c7:c8:c9:c10 a__x :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c8 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c6:c7:c8:c9:c10 c9 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c6:c7:c8:c9:c10 c10 :: c6:c7:c8:c9:c10 and :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c11 :: c:c1 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 plus :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c12 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 c13 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 x :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c14 :: c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 c15 :: c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 c16 :: c11:c12:c13:c14:c15:c16:c17:c18 c17 :: c11:c12:c13:c14:c15:c16:c17:c18 c18 :: c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 a__and :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x a__plus :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x hole_c:c11_19 :: c:c1 hole_tt:0':s:and:plus:x2_19 :: tt:0':s:and:plus:x hole_c11:c12:c13:c14:c15:c16:c17:c183_19 :: c11:c12:c13:c14:c15:c16:c17:c18 hole_c2:c3:c4:c54_19 :: c2:c3:c4:c5 hole_c6:c7:c8:c9:c105_19 :: c6:c7:c8:c9:c10 gen_tt:0':s:and:plus:x6_19 :: Nat -> tt:0':s:and:plus:x gen_c11:c12:c13:c14:c15:c16:c17:c187_19 :: Nat -> c11:c12:c13:c14:c15:c16:c17:c18 gen_c2:c3:c4:c58_19 :: Nat -> c2:c3:c4:c5 gen_c6:c7:c8:c9:c109_19 :: Nat -> c6:c7:c8:c9:c10 Lemmas: mark(gen_tt:0':s:and:plus:x6_19(n25340_19)) -> gen_tt:0':s:and:plus:x6_19(n25340_19), rt in Omega(0) a__x(gen_tt:0':s:and:plus:x6_19(a), gen_tt:0':s:and:plus:x6_19(+(1, n26807_19))) -> *10_19, rt in Omega(0) a__plus(gen_tt:0':s:and:plus:x6_19(a), gen_tt:0':s:and:plus:x6_19(+(1, n21738_19))) -> *10_19, rt in Omega(0) Generator Equations: gen_tt:0':s:and:plus:x6_19(0) <=> tt gen_tt:0':s:and:plus:x6_19(+(x, 1)) <=> s(gen_tt:0':s:and:plus:x6_19(x)) gen_c11:c12:c13:c14:c15:c16:c17:c187_19(0) <=> c16 gen_c11:c12:c13:c14:c15:c16:c17:c187_19(+(x, 1)) <=> c11(c(c16), gen_c11:c12:c13:c14:c15:c16:c17:c187_19(x)) gen_c2:c3:c4:c58_19(0) <=> c2(c16) gen_c2:c3:c4:c58_19(+(x, 1)) <=> c3(gen_c2:c3:c4:c58_19(x), c16) gen_c6:c7:c8:c9:c109_19(0) <=> c6 gen_c6:c7:c8:c9:c109_19(+(x, 1)) <=> c7(c2(c16), gen_c6:c7:c8:c9:c109_19(x), c16) The following defined symbols remain to be analysed: A__PLUS, MARK, A__X They will be analysed ascendingly in the following order: MARK = A__PLUS MARK = A__X A__PLUS = A__X ---------------------------------------- (28) LowerBoundPropagationProof (FINISHED) Propagated lower bound. ---------------------------------------- (29) BOUNDS(n^1, INF) ---------------------------------------- (30) 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 A__X(z0, 0') -> c6 A__X(z0, s(z1)) -> c7(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z0)) A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) A__X(z0, z1) -> c10 MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c16 MARK(0') -> c17 MARK(s(z0)) -> c18(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) a__x(z0, 0') -> 0' a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(0') -> 0' mark(s(z0)) -> s(mark(z0)) Types: A__AND :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> c:c1 tt :: tt:0':s:and:plus:x c :: c11:c12:c13:c14:c15:c16:c17:c18 -> c:c1 MARK :: tt:0':s:and:plus:x -> c11:c12:c13:c14:c15:c16:c17:c18 c1 :: c:c1 A__PLUS :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> c2:c3:c4:c5 0' :: tt:0':s:and:plus:x c2 :: c11:c12:c13:c14:c15:c16:c17:c18 -> c2:c3:c4:c5 s :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x c3 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c2:c3:c4:c5 mark :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x c4 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c2:c3:c4:c5 c5 :: c2:c3:c4:c5 A__X :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> c6:c7:c8:c9:c10 c6 :: c6:c7:c8:c9:c10 c7 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c6:c7:c8:c9:c10 a__x :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c8 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c6:c7:c8:c9:c10 c9 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c6:c7:c8:c9:c10 c10 :: c6:c7:c8:c9:c10 and :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c11 :: c:c1 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 plus :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c12 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 c13 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 x :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c14 :: c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 c15 :: c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 c16 :: c11:c12:c13:c14:c15:c16:c17:c18 c17 :: c11:c12:c13:c14:c15:c16:c17:c18 c18 :: c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 a__and :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x a__plus :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x hole_c:c11_19 :: c:c1 hole_tt:0':s:and:plus:x2_19 :: tt:0':s:and:plus:x hole_c11:c12:c13:c14:c15:c16:c17:c183_19 :: c11:c12:c13:c14:c15:c16:c17:c18 hole_c2:c3:c4:c54_19 :: c2:c3:c4:c5 hole_c6:c7:c8:c9:c105_19 :: c6:c7:c8:c9:c10 gen_tt:0':s:and:plus:x6_19 :: Nat -> tt:0':s:and:plus:x gen_c11:c12:c13:c14:c15:c16:c17:c187_19 :: Nat -> c11:c12:c13:c14:c15:c16:c17:c18 gen_c2:c3:c4:c58_19 :: Nat -> c2:c3:c4:c5 gen_c6:c7:c8:c9:c109_19 :: Nat -> c6:c7:c8:c9:c10 Lemmas: mark(gen_tt:0':s:and:plus:x6_19(n25340_19)) -> gen_tt:0':s:and:plus:x6_19(n25340_19), rt in Omega(0) a__x(gen_tt:0':s:and:plus:x6_19(a), gen_tt:0':s:and:plus:x6_19(+(1, n26807_19))) -> *10_19, rt in Omega(0) a__plus(gen_tt:0':s:and:plus:x6_19(a), gen_tt:0':s:and:plus:x6_19(+(1, n21738_19))) -> *10_19, rt in Omega(0) A__PLUS(gen_tt:0':s:and:plus:x6_19(a), gen_tt:0':s:and:plus:x6_19(+(1, n35904_19))) -> *10_19, rt in Omega(n35904_19) Generator Equations: gen_tt:0':s:and:plus:x6_19(0) <=> tt gen_tt:0':s:and:plus:x6_19(+(x, 1)) <=> s(gen_tt:0':s:and:plus:x6_19(x)) gen_c11:c12:c13:c14:c15:c16:c17:c187_19(0) <=> c16 gen_c11:c12:c13:c14:c15:c16:c17:c187_19(+(x, 1)) <=> c11(c(c16), gen_c11:c12:c13:c14:c15:c16:c17:c187_19(x)) gen_c2:c3:c4:c58_19(0) <=> c2(c16) gen_c2:c3:c4:c58_19(+(x, 1)) <=> c3(gen_c2:c3:c4:c58_19(x), c16) gen_c6:c7:c8:c9:c109_19(0) <=> c6 gen_c6:c7:c8:c9:c109_19(+(x, 1)) <=> c7(c2(c16), gen_c6:c7:c8:c9:c109_19(x), c16) The following defined symbols remain to be analysed: MARK, A__X They will be analysed ascendingly in the following order: MARK = A__PLUS MARK = A__X A__PLUS = A__X ---------------------------------------- (31) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: MARK(gen_tt:0':s:and:plus:x6_19(+(1, n45034_19))) -> *10_19, rt in Omega(n45034_19) Induction Base: MARK(gen_tt:0':s:and:plus:x6_19(+(1, 0))) Induction Step: MARK(gen_tt:0':s:and:plus:x6_19(+(1, +(n45034_19, 1)))) ->_R^Omega(1) c18(MARK(gen_tt:0':s:and:plus:x6_19(+(1, n45034_19)))) ->_IH c18(*10_19) We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (32) 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 A__X(z0, 0') -> c6 A__X(z0, s(z1)) -> c7(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z0)) A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) A__X(z0, z1) -> c10 MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c16 MARK(0') -> c17 MARK(s(z0)) -> c18(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) a__x(z0, 0') -> 0' a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(0') -> 0' mark(s(z0)) -> s(mark(z0)) Types: A__AND :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> c:c1 tt :: tt:0':s:and:plus:x c :: c11:c12:c13:c14:c15:c16:c17:c18 -> c:c1 MARK :: tt:0':s:and:plus:x -> c11:c12:c13:c14:c15:c16:c17:c18 c1 :: c:c1 A__PLUS :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> c2:c3:c4:c5 0' :: tt:0':s:and:plus:x c2 :: c11:c12:c13:c14:c15:c16:c17:c18 -> c2:c3:c4:c5 s :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x c3 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c2:c3:c4:c5 mark :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x c4 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c2:c3:c4:c5 c5 :: c2:c3:c4:c5 A__X :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> c6:c7:c8:c9:c10 c6 :: c6:c7:c8:c9:c10 c7 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c6:c7:c8:c9:c10 a__x :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c8 :: c2:c3:c4:c5 -> c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c6:c7:c8:c9:c10 c9 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c6:c7:c8:c9:c10 c10 :: c6:c7:c8:c9:c10 and :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c11 :: c:c1 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 plus :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c12 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 c13 :: c2:c3:c4:c5 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 x :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x c14 :: c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 c15 :: c6:c7:c8:c9:c10 -> c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 c16 :: c11:c12:c13:c14:c15:c16:c17:c18 c17 :: c11:c12:c13:c14:c15:c16:c17:c18 c18 :: c11:c12:c13:c14:c15:c16:c17:c18 -> c11:c12:c13:c14:c15:c16:c17:c18 a__and :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x a__plus :: tt:0':s:and:plus:x -> tt:0':s:and:plus:x -> tt:0':s:and:plus:x hole_c:c11_19 :: c:c1 hole_tt:0':s:and:plus:x2_19 :: tt:0':s:and:plus:x hole_c11:c12:c13:c14:c15:c16:c17:c183_19 :: c11:c12:c13:c14:c15:c16:c17:c18 hole_c2:c3:c4:c54_19 :: c2:c3:c4:c5 hole_c6:c7:c8:c9:c105_19 :: c6:c7:c8:c9:c10 gen_tt:0':s:and:plus:x6_19 :: Nat -> tt:0':s:and:plus:x gen_c11:c12:c13:c14:c15:c16:c17:c187_19 :: Nat -> c11:c12:c13:c14:c15:c16:c17:c18 gen_c2:c3:c4:c58_19 :: Nat -> c2:c3:c4:c5 gen_c6:c7:c8:c9:c109_19 :: Nat -> c6:c7:c8:c9:c10 Lemmas: mark(gen_tt:0':s:and:plus:x6_19(n25340_19)) -> gen_tt:0':s:and:plus:x6_19(n25340_19), rt in Omega(0) a__x(gen_tt:0':s:and:plus:x6_19(a), gen_tt:0':s:and:plus:x6_19(+(1, n26807_19))) -> *10_19, rt in Omega(0) a__plus(gen_tt:0':s:and:plus:x6_19(a), gen_tt:0':s:and:plus:x6_19(+(1, n21738_19))) -> *10_19, rt in Omega(0) A__PLUS(gen_tt:0':s:and:plus:x6_19(a), gen_tt:0':s:and:plus:x6_19(+(1, n35904_19))) -> *10_19, rt in Omega(n35904_19) MARK(gen_tt:0':s:and:plus:x6_19(+(1, n45034_19))) -> *10_19, rt in Omega(n45034_19) Generator Equations: gen_tt:0':s:and:plus:x6_19(0) <=> tt gen_tt:0':s:and:plus:x6_19(+(x, 1)) <=> s(gen_tt:0':s:and:plus:x6_19(x)) gen_c11:c12:c13:c14:c15:c16:c17:c187_19(0) <=> c16 gen_c11:c12:c13:c14:c15:c16:c17:c187_19(+(x, 1)) <=> c11(c(c16), gen_c11:c12:c13:c14:c15:c16:c17:c187_19(x)) gen_c2:c3:c4:c58_19(0) <=> c2(c16) gen_c2:c3:c4:c58_19(+(x, 1)) <=> c3(gen_c2:c3:c4:c58_19(x), c16) gen_c6:c7:c8:c9:c109_19(0) <=> c6 gen_c6:c7:c8:c9:c109_19(+(x, 1)) <=> c7(c2(c16), gen_c6:c7:c8:c9:c109_19(x), c16) The following defined symbols remain to be analysed: A__X, A__PLUS They will be analysed ascendingly in the following order: MARK = A__PLUS MARK = A__X A__PLUS = A__X ---------------------------------------- (33) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: A__PLUS(gen_tt:0':s:and:plus:x6_19(a), gen_tt:0':s:and:plus:x6_19(+(1, n70317_19))) -> *10_19, rt in Omega(n70317_19) Induction Base: A__PLUS(gen_tt:0':s:and:plus:x6_19(a), gen_tt:0':s:and:plus:x6_19(+(1, 0))) Induction Step: A__PLUS(gen_tt:0':s:and:plus:x6_19(a), gen_tt:0':s:and:plus:x6_19(+(1, +(n70317_19, 1)))) ->_R^Omega(1) c3(A__PLUS(mark(gen_tt:0':s:and:plus:x6_19(a)), mark(gen_tt:0':s:and:plus:x6_19(+(1, n70317_19)))), MARK(gen_tt:0':s:and:plus:x6_19(a))) ->_L^Omega(0) c3(A__PLUS(gen_tt:0':s:and:plus:x6_19(a), mark(gen_tt:0':s:and:plus:x6_19(+(1, n70317_19)))), MARK(gen_tt:0':s:and:plus:x6_19(a))) ->_L^Omega(0) c3(A__PLUS(gen_tt:0':s:and:plus:x6_19(a), gen_tt:0':s:and:plus:x6_19(+(1, n70317_19))), MARK(gen_tt:0':s:and:plus:x6_19(a))) ->_IH c3(*10_19, MARK(gen_tt:0':s:and:plus:x6_19(a))) We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (34) BOUNDS(1, INF) ---------------------------------------- (35) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (36) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__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] a__x(N, 0) -> 0 [1] a__x(N, s(M)) -> a__plus(a__x(mark(N), mark(M)), mark(N)) [1] mark(and(X1, X2)) -> a__and(mark(X1), X2) [1] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(x(X1, X2)) -> a__x(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] a__x(X1, X2) -> x(X1, X2) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (37) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (38) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__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] a__x(N, 0) -> 0 [1] a__x(N, s(M)) -> a__plus(a__x(mark(N), mark(M)), mark(N)) [1] mark(and(X1, X2)) -> a__and(mark(X1), X2) [1] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(x(X1, X2)) -> a__x(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] a__x(X1, X2) -> x(X1, X2) [1] The TRS has the following type information: a__and :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x -> tt:0:s:and:plus:x tt :: tt:0:s:and:plus:x mark :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x a__plus :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x -> tt:0:s:and:plus:x 0 :: tt:0:s:and:plus:x s :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x a__x :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x -> tt:0:s:and:plus:x and :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x -> tt:0:s:and:plus:x plus :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x -> tt:0:s:and:plus:x x :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x -> tt:0:s:and:plus:x Rewrite Strategy: INNERMOST ---------------------------------------- (39) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: none (c) The following functions are completely defined: mark_1 a__x_2 a__and_2 a__plus_2 Due to the following rules being added: none And the following fresh constants: none ---------------------------------------- (40) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__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] a__x(N, 0) -> 0 [1] a__x(N, s(M)) -> a__plus(a__x(mark(N), mark(M)), mark(N)) [1] mark(and(X1, X2)) -> a__and(mark(X1), X2) [1] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(x(X1, X2)) -> a__x(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] a__x(X1, X2) -> x(X1, X2) [1] The TRS has the following type information: a__and :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x -> tt:0:s:and:plus:x tt :: tt:0:s:and:plus:x mark :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x a__plus :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x -> tt:0:s:and:plus:x 0 :: tt:0:s:and:plus:x s :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x a__x :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x -> tt:0:s:and:plus:x and :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x -> tt:0:s:and:plus:x plus :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x -> tt:0:s:and:plus:x x :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x -> tt:0:s:and:plus:x Rewrite Strategy: INNERMOST ---------------------------------------- (41) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (42) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__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] a__x(N, 0) -> 0 [1] a__x(N, s(M)) -> a__plus(a__x(mark(N), mark(M)), mark(N)) [1] mark(and(and(X141, X241), X2)) -> a__and(a__and(mark(X141), X241), X2) [2] mark(and(plus(X142, X242), X2)) -> a__and(a__plus(mark(X142), mark(X242)), X2) [2] mark(and(x(X143, X243), X2)) -> a__and(a__x(mark(X143), mark(X243)), X2) [2] mark(and(tt, X2)) -> a__and(tt, X2) [2] mark(and(0, X2)) -> a__and(0, X2) [2] mark(and(s(X33), X2)) -> a__and(s(mark(X33)), X2) [2] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(x(X1, X2)) -> a__x(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] a__x(X1, X2) -> x(X1, X2) [1] The TRS has the following type information: a__and :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x -> tt:0:s:and:plus:x tt :: tt:0:s:and:plus:x mark :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x a__plus :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x -> tt:0:s:and:plus:x 0 :: tt:0:s:and:plus:x s :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x a__x :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x -> tt:0:s:and:plus:x and :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x -> tt:0:s:and:plus:x plus :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x -> tt:0:s:and:plus:x x :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x -> tt:0:s:and:plus:x Rewrite Strategy: INNERMOST ---------------------------------------- (43) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: tt => 1 0 => 0 ---------------------------------------- (44) Obligation: Complexity RNTS consisting of the following rules: a__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 a__x(z, z') -{ 1 }-> a__plus(a__x(mark(N), mark(M)), mark(N)) :|: z' = 1 + M, z = N, M >= 0, N >= 0 a__x(z, z') -{ 1 }-> 0 :|: z = N, z' = 0, N >= 0 a__x(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 mark(z) -{ 1 }-> a__x(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__plus(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> a__and(a__x(mark(X143), mark(X243)), X2) :|: z = 1 + (1 + X143 + X243) + X2, X243 >= 0, X143 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__plus(mark(X142), mark(X242)), X2) :|: z = 1 + (1 + X142 + X242) + X2, X242 >= 0, X2 >= 0, X142 >= 0 mark(z) -{ 2 }-> a__and(a__and(mark(X141), X241), X2) :|: z = 1 + (1 + X141 + X241) + X2, X241 >= 0, X2 >= 0, X141 >= 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(X33), X2) :|: X33 >= 0, z = 1 + (1 + X33) + X2, 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 ---------------------------------------- (45) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (46) Obligation: Complexity RNTS consisting of the following rules: a__and(z, z') -{ 1 }-> 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 a__x(z, z') -{ 1 }-> a__plus(a__x(mark(z), mark(z' - 1)), mark(z)) :|: z' - 1 >= 0, z >= 0 a__x(z, z') -{ 1 }-> 0 :|: z' = 0, z >= 0 a__x(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 mark(z) -{ 1 }-> a__x(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__plus(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> a__and(a__x(mark(X143), mark(X243)), X2) :|: z = 1 + (1 + X143 + X243) + X2, X243 >= 0, X143 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__and(a__plus(mark(X142), mark(X242)), X2) :|: z = 1 + (1 + X142 + X242) + X2, X242 >= 0, X2 >= 0, X142 >= 0 mark(z) -{ 2 }-> a__and(a__and(mark(X141), X241), X2) :|: z = 1 + (1 + X141 + X241) + X2, X241 >= 0, X2 >= 0, X141 >= 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(X33), X2) :|: X33 >= 0, z = 1 + (1 + X33) + X2, X2 >= 0 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(z - 1) :|: z - 1 >= 0 ---------------------------------------- (47) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: none And the following fresh constants: none ---------------------------------------- (48) Obligation: Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__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] a__x(N, 0) -> 0 [1] a__x(N, s(M)) -> a__plus(a__x(mark(N), mark(M)), mark(N)) [1] mark(and(X1, X2)) -> a__and(mark(X1), X2) [1] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(x(X1, X2)) -> a__x(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] a__x(X1, X2) -> x(X1, X2) [1] The TRS has the following type information: a__and :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x -> tt:0:s:and:plus:x tt :: tt:0:s:and:plus:x mark :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x a__plus :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x -> tt:0:s:and:plus:x 0 :: tt:0:s:and:plus:x s :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x a__x :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x -> tt:0:s:and:plus:x and :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x -> tt:0:s:and:plus:x plus :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x -> tt:0:s:and:plus:x x :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x -> tt:0:s:and:plus:x Rewrite Strategy: INNERMOST ---------------------------------------- (49) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: tt => 1 0 => 0 ---------------------------------------- (50) 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 a__x(z, z') -{ 1 }-> a__plus(a__x(mark(N), mark(M)), mark(N)) :|: z' = 1 + M, z = N, M >= 0, N >= 0 a__x(z, z') -{ 1 }-> 0 :|: z = N, z' = 0, N >= 0 a__x(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 mark(z) -{ 1 }-> a__x(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + 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. ---------------------------------------- (51) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (52) 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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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 A__X(z0, 0) -> c6 A__X(z0, s(z1)) -> c7(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z0)) A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) A__X(z0, z1) -> c10 MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c16 MARK(0) -> c17 MARK(s(z0)) -> c18(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 A__X(z0, 0) -> c6 A__X(z0, s(z1)) -> c7(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z0)) A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) A__X(z0, z1) -> c10 MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c16 MARK(0) -> c17 MARK(s(z0)) -> c18(MARK(z0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, A__X_2, MARK_1 Compound Symbols: c_1, c1, c2_1, c3_2, c4_2, c5, c6, c7_3, c8_3, c9_2, c10, c11_2, c12_2, c13_2, c14_2, c15_2, c16, c17, c18_1 ---------------------------------------- (53) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing nodes: A__X(z0, z1) -> c10 A__PLUS(z0, z1) -> c5 A__AND(z0, z1) -> c1 MARK(0) -> c17 MARK(tt) -> c16 A__X(z0, 0) -> c6 ---------------------------------------- (54) 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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) A__X(z0, s(z1)) -> c7(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z0)) A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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)) A__X(z0, s(z1)) -> c7(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z0)) A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(MARK(z0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, A__X_2, MARK_1 Compound Symbols: c_1, c2_1, c3_2, c4_2, c7_3, c8_3, c9_2, c11_2, c12_2, c13_2, c14_2, c15_2, c18_1 ---------------------------------------- (55) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (56) 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)) A__X(z0, s(z1)) -> c7(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z0)) A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Rewrite Strategy: INNERMOST ---------------------------------------- (57) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (58) 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)) A__X(z0, s(z1)) -> c7(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z0)) A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (59) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (60) 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] A__X(z0, s(z1)) -> c7(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z0)) [1] A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) [1] A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) [1] MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) [1] MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) [1] MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) [1] MARK(s(z0)) -> c18(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] a__x(z0, 0) -> 0 [0] a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) [0] a__x(z0, z1) -> x(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(x(z0, z1)) -> a__x(mark(z0), mark(z1)) [0] mark(tt) -> tt [0] mark(0) -> 0 [0] mark(s(z0)) -> s(mark(z0)) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (61) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (62) 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] A__X(z0, s(z1)) -> c7(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z0)) [1] A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) [1] A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) [1] MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) [1] MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) [1] MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) [1] MARK(s(z0)) -> c18(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] a__x(z0, 0) -> 0 [0] a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) [0] a__x(z0, z1) -> x(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(x(z0, z1)) -> a__x(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:x -> tt:0:s:and:plus:x -> c tt :: tt:0:s:and:plus:x c :: c11:c12:c13:c14:c15:c18 -> c MARK :: tt:0:s:and:plus:x -> c11:c12:c13:c14:c15:c18 A__PLUS :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x -> c2:c3:c4 0 :: tt:0:s:and:plus:x c2 :: c11:c12:c13:c14:c15:c18 -> c2:c3:c4 s :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x c3 :: c2:c3:c4 -> c11:c12:c13:c14:c15:c18 -> c2:c3:c4 mark :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x c4 :: c2:c3:c4 -> c11:c12:c13:c14:c15:c18 -> c2:c3:c4 A__X :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x -> c7:c8:c9 c7 :: c2:c3:c4 -> c7:c8:c9 -> c11:c12:c13:c14:c15:c18 -> c7:c8:c9 a__x :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x -> tt:0:s:and:plus:x c8 :: c2:c3:c4 -> c7:c8:c9 -> c11:c12:c13:c14:c15:c18 -> c7:c8:c9 c9 :: c2:c3:c4 -> c11:c12:c13:c14:c15:c18 -> c7:c8:c9 and :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x -> tt:0:s:and:plus:x c11 :: c -> c11:c12:c13:c14:c15:c18 -> c11:c12:c13:c14:c15:c18 plus :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x -> tt:0:s:and:plus:x c12 :: c2:c3:c4 -> c11:c12:c13:c14:c15:c18 -> c11:c12:c13:c14:c15:c18 c13 :: c2:c3:c4 -> c11:c12:c13:c14:c15:c18 -> c11:c12:c13:c14:c15:c18 x :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x -> tt:0:s:and:plus:x c14 :: c7:c8:c9 -> c11:c12:c13:c14:c15:c18 -> c11:c12:c13:c14:c15:c18 c15 :: c7:c8:c9 -> c11:c12:c13:c14:c15:c18 -> c11:c12:c13:c14:c15:c18 c18 :: c11:c12:c13:c14:c15:c18 -> c11:c12:c13:c14:c15:c18 a__and :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x -> tt:0:s:and:plus:x a__plus :: tt:0:s:and:plus:x -> tt:0:s:and:plus:x -> tt:0:s:and:plus:x Rewrite Strategy: INNERMOST ---------------------------------------- (63) 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 A__X_2 MARK_1 (c) The following functions are completely defined: a__and_2 a__plus_2 a__x_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] a__x(v0, v1) -> null_a__x [0] mark(v0) -> null_mark [0] And the following fresh constants: null_a__and, null_a__plus, null_a__x, null_mark, const, const1, const2, const3 ---------------------------------------- (64) 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] A__X(z0, s(z1)) -> c7(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z0)) [1] A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) [1] A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) [1] MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) [1] MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) [1] MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) [1] MARK(s(z0)) -> c18(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] a__x(z0, 0) -> 0 [0] a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) [0] a__x(z0, z1) -> x(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(x(z0, z1)) -> a__x(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] a__x(v0, v1) -> null_a__x [0] mark(v0) -> null_mark [0] The TRS has the following type information: A__AND :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> c tt :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark c :: c11:c12:c13:c14:c15:c18 -> c MARK :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> c11:c12:c13:c14:c15:c18 A__PLUS :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> c2:c3:c4 0 :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark c2 :: c11:c12:c13:c14:c15:c18 -> c2:c3:c4 s :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark c3 :: c2:c3:c4 -> c11:c12:c13:c14:c15:c18 -> c2:c3:c4 mark :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark c4 :: c2:c3:c4 -> c11:c12:c13:c14:c15:c18 -> c2:c3:c4 A__X :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> c7:c8:c9 c7 :: c2:c3:c4 -> c7:c8:c9 -> c11:c12:c13:c14:c15:c18 -> c7:c8:c9 a__x :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark c8 :: c2:c3:c4 -> c7:c8:c9 -> c11:c12:c13:c14:c15:c18 -> c7:c8:c9 c9 :: c2:c3:c4 -> c11:c12:c13:c14:c15:c18 -> c7:c8:c9 and :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark c11 :: c -> c11:c12:c13:c14:c15:c18 -> c11:c12:c13:c14:c15:c18 plus :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark c12 :: c2:c3:c4 -> c11:c12:c13:c14:c15:c18 -> c11:c12:c13:c14:c15:c18 c13 :: c2:c3:c4 -> c11:c12:c13:c14:c15:c18 -> c11:c12:c13:c14:c15:c18 x :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark c14 :: c7:c8:c9 -> c11:c12:c13:c14:c15:c18 -> c11:c12:c13:c14:c15:c18 c15 :: c7:c8:c9 -> c11:c12:c13:c14:c15:c18 -> c11:c12:c13:c14:c15:c18 c18 :: c11:c12:c13:c14:c15:c18 -> c11:c12:c13:c14:c15:c18 a__and :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark a__plus :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark null_a__and :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark null_a__plus :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark null_a__x :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark null_mark :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark const :: c const1 :: c11:c12:c13:c14:c15:c18 const2 :: c2:c3:c4 const3 :: c7:c8:c9 Rewrite Strategy: INNERMOST ---------------------------------------- (65) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (66) 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] A__X(z0, s(z1)) -> c7(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z0)) [1] A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) [1] A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) [1] MARK(and(and(z0643, z1482), z1)) -> c11(A__AND(a__and(mark(z0643), z1482), z1), MARK(and(z0643, z1482))) [1] MARK(and(plus(z0644, z1483), z1)) -> c11(A__AND(a__plus(mark(z0644), mark(z1483)), z1), MARK(plus(z0644, z1483))) [1] MARK(and(x(z0645, z1484), z1)) -> c11(A__AND(a__x(mark(z0645), mark(z1484)), z1), MARK(x(z0645, z1484))) [1] MARK(and(tt, z1)) -> c11(A__AND(tt, z1), MARK(tt)) [1] MARK(and(0, z1)) -> c11(A__AND(0, z1), MARK(0)) [1] MARK(and(s(z0646), z1)) -> c11(A__AND(s(mark(z0646)), z1), MARK(s(z0646))) [1] MARK(and(z0, z1)) -> c11(A__AND(null_mark, z1), MARK(z0)) [1] MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) [1] MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) [1] MARK(s(z0)) -> c18(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] a__x(z0, 0) -> 0 [0] a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) [0] a__x(z0, z1) -> x(z0, z1) [0] mark(and(and(z0867, z1650), z1)) -> a__and(a__and(mark(z0867), z1650), z1) [0] mark(and(plus(z0868, z1651), z1)) -> a__and(a__plus(mark(z0868), mark(z1651)), z1) [0] mark(and(x(z0869, z1652), z1)) -> a__and(a__x(mark(z0869), mark(z1652)), z1) [0] mark(and(tt, z1)) -> a__and(tt, z1) [0] mark(and(0, z1)) -> a__and(0, z1) [0] mark(and(s(z0870), z1)) -> a__and(s(mark(z0870)), z1) [0] mark(and(z0, z1)) -> a__and(null_mark, z1) [0] mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0] mark(x(z0, z1)) -> a__x(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] a__x(v0, v1) -> null_a__x [0] mark(v0) -> null_mark [0] The TRS has the following type information: A__AND :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> c tt :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark c :: c11:c12:c13:c14:c15:c18 -> c MARK :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> c11:c12:c13:c14:c15:c18 A__PLUS :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> c2:c3:c4 0 :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark c2 :: c11:c12:c13:c14:c15:c18 -> c2:c3:c4 s :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark c3 :: c2:c3:c4 -> c11:c12:c13:c14:c15:c18 -> c2:c3:c4 mark :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark c4 :: c2:c3:c4 -> c11:c12:c13:c14:c15:c18 -> c2:c3:c4 A__X :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> c7:c8:c9 c7 :: c2:c3:c4 -> c7:c8:c9 -> c11:c12:c13:c14:c15:c18 -> c7:c8:c9 a__x :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark c8 :: c2:c3:c4 -> c7:c8:c9 -> c11:c12:c13:c14:c15:c18 -> c7:c8:c9 c9 :: c2:c3:c4 -> c11:c12:c13:c14:c15:c18 -> c7:c8:c9 and :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark c11 :: c -> c11:c12:c13:c14:c15:c18 -> c11:c12:c13:c14:c15:c18 plus :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark c12 :: c2:c3:c4 -> c11:c12:c13:c14:c15:c18 -> c11:c12:c13:c14:c15:c18 c13 :: c2:c3:c4 -> c11:c12:c13:c14:c15:c18 -> c11:c12:c13:c14:c15:c18 x :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark c14 :: c7:c8:c9 -> c11:c12:c13:c14:c15:c18 -> c11:c12:c13:c14:c15:c18 c15 :: c7:c8:c9 -> c11:c12:c13:c14:c15:c18 -> c11:c12:c13:c14:c15:c18 c18 :: c11:c12:c13:c14:c15:c18 -> c11:c12:c13:c14:c15:c18 a__and :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark a__plus :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark null_a__and :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark null_a__plus :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark null_a__x :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark null_mark :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark const :: c const1 :: c11:c12:c13:c14:c15:c18 const2 :: c2:c3:c4 const3 :: c7:c8:c9 Rewrite Strategy: INNERMOST ---------------------------------------- (67) 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_a__x => 0 null_mark => 0 const => 0 const1 => 0 const2 => 0 const3 => 0 ---------------------------------------- (68) 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 A__X(z, z') -{ 1 }-> 1 + A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)) + MARK(z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 A__X(z, z') -{ 1 }-> 1 + A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)) + A__X(mark(z0), mark(z1)) + MARK(z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 A__X(z, z') -{ 1 }-> 1 + A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)) + A__X(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__X(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__X(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__AND(a__x(mark(z0645), mark(z1484)), z1) + MARK(1 + z0645 + z1484) :|: z0645 >= 0, z1 >= 0, z = 1 + (1 + z0645 + z1484) + z1, z1484 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__plus(mark(z0644), mark(z1483)), z1) + MARK(1 + z0644 + z1483) :|: z1 >= 0, z1483 >= 0, z = 1 + (1 + z0644 + z1483) + z1, z0644 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__and(mark(z0643), z1482), z1) + MARK(1 + z0643 + z1482) :|: z1 >= 0, z1482 >= 0, z = 1 + (1 + z0643 + z1482) + z1, z0643 >= 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(z0646), z1) + MARK(1 + z0646) :|: z1 >= 0, z = 1 + (1 + z0646) + z1, z0646 >= 0 a__and(z, z') -{ 0 }-> mark(z0) :|: z = 1, z0 >= 0, z' = z0 a__and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__and(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__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 a__x(z, z') -{ 0 }-> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 a__x(z, z') -{ 0 }-> 0 :|: z = z0, z0 >= 0, z' = 0 a__x(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__x(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 mark(z) -{ 0 }-> a__x(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__plus(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__and(a__x(mark(z0869), mark(z1652)), z1) :|: z = 1 + (1 + z0869 + z1652) + z1, z1 >= 0, z0869 >= 0, z1652 >= 0 mark(z) -{ 0 }-> a__and(a__plus(mark(z0868), mark(z1651)), z1) :|: z0868 >= 0, z1 >= 0, z1651 >= 0, z = 1 + (1 + z0868 + z1651) + z1 mark(z) -{ 0 }-> a__and(a__and(mark(z0867), z1650), z1) :|: z1650 >= 0, z1 >= 0, z0867 >= 0, z = 1 + (1 + z0867 + z1650) + z1 mark(z) -{ 0 }-> a__and(1, z1) :|: z1 >= 0, z = 1 + 1 + z1 mark(z) -{ 0 }-> a__and(0, z1) :|: z1 >= 0, z = 1 + 0 + z1 mark(z) -{ 0 }-> a__and(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__and(1 + mark(z0870), z1) :|: z = 1 + (1 + z0870) + z1, z0870 >= 0, z1 >= 0 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0 ---------------------------------------- (69) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (70) 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 A__X(z, z') -{ 1 }-> 1 + A__PLUS(a__x(mark(z), mark(z' - 1)), mark(z)) + MARK(z) :|: z' - 1 >= 0, z >= 0 A__X(z, z') -{ 1 }-> 1 + A__PLUS(a__x(mark(z), mark(z' - 1)), mark(z)) + A__X(mark(z), mark(z' - 1)) + MARK(z) :|: z' - 1 >= 0, z >= 0 A__X(z, z') -{ 1 }-> 1 + A__PLUS(a__x(mark(z), mark(z' - 1)), mark(z)) + A__X(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__X(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__X(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__AND(a__x(mark(z0645), mark(z1484)), z1) + MARK(1 + z0645 + z1484) :|: z0645 >= 0, z1 >= 0, z = 1 + (1 + z0645 + z1484) + z1, z1484 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__plus(mark(z0644), mark(z1483)), z1) + MARK(1 + z0644 + z1483) :|: z1 >= 0, z1483 >= 0, z = 1 + (1 + z0644 + z1483) + z1, z0644 >= 0 MARK(z) -{ 1 }-> 1 + A__AND(a__and(mark(z0643), z1482), z1) + MARK(1 + z0643 + z1482) :|: z1 >= 0, z1482 >= 0, z = 1 + (1 + z0643 + z1482) + z1, z0643 >= 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(z0646), z1) + MARK(1 + z0646) :|: z1 >= 0, z = 1 + (1 + z0646) + z1, z0646 >= 0 a__and(z, z') -{ 0 }-> mark(z') :|: z = 1, z' >= 0 a__and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__and(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__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 a__x(z, z') -{ 0 }-> a__plus(a__x(mark(z), mark(z' - 1)), mark(z)) :|: z' - 1 >= 0, z >= 0 a__x(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0 a__x(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__x(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 mark(z) -{ 0 }-> a__x(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__plus(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__and(a__x(mark(z0869), mark(z1652)), z1) :|: z = 1 + (1 + z0869 + z1652) + z1, z1 >= 0, z0869 >= 0, z1652 >= 0 mark(z) -{ 0 }-> a__and(a__plus(mark(z0868), mark(z1651)), z1) :|: z0868 >= 0, z1 >= 0, z1651 >= 0, z = 1 + (1 + z0868 + z1651) + z1 mark(z) -{ 0 }-> a__and(a__and(mark(z0867), z1650), z1) :|: z1650 >= 0, z1 >= 0, z0867 >= 0, z = 1 + (1 + z0867 + z1650) + z1 mark(z) -{ 0 }-> a__and(1, z - 2) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__and(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__and(0, z - 1) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__and(1 + mark(z0870), z1) :|: z = 1 + (1 + z0870) + z1, z0870 >= 0, z1 >= 0 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 ---------------------------------------- (71) 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] a__x(v0, v1) -> null_a__x [0] mark(v0) -> null_mark [0] A__AND(v0, v1) -> null_A__AND [0] A__PLUS(v0, v1) -> null_A__PLUS [0] A__X(v0, v1) -> null_A__X [0] MARK(v0) -> null_MARK [0] And the following fresh constants: null_a__and, null_a__plus, null_a__x, null_mark, null_A__AND, null_A__PLUS, null_A__X, null_MARK ---------------------------------------- (72) 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] A__X(z0, s(z1)) -> c7(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z0)) [1] A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) [1] A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) [1] MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) [1] MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) [1] MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) [1] MARK(s(z0)) -> c18(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] a__x(z0, 0) -> 0 [0] a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) [0] a__x(z0, z1) -> x(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(x(z0, z1)) -> a__x(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] a__x(v0, v1) -> null_a__x [0] mark(v0) -> null_mark [0] A__AND(v0, v1) -> null_A__AND [0] A__PLUS(v0, v1) -> null_A__PLUS [0] A__X(v0, v1) -> null_A__X [0] MARK(v0) -> null_MARK [0] The TRS has the following type information: A__AND :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> c:null_A__AND tt :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark c :: c11:c12:c13:c14:c15:c18:null_MARK -> c:null_A__AND MARK :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> c11:c12:c13:c14:c15:c18:null_MARK A__PLUS :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> c2:c3:c4:null_A__PLUS 0 :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark c2 :: c11:c12:c13:c14:c15:c18:null_MARK -> c2:c3:c4:null_A__PLUS s :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark c3 :: c2:c3:c4:null_A__PLUS -> c11:c12:c13:c14:c15:c18:null_MARK -> c2:c3:c4:null_A__PLUS mark :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark c4 :: c2:c3:c4:null_A__PLUS -> c11:c12:c13:c14:c15:c18:null_MARK -> c2:c3:c4:null_A__PLUS A__X :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> c7:c8:c9:null_A__X c7 :: c2:c3:c4:null_A__PLUS -> c7:c8:c9:null_A__X -> c11:c12:c13:c14:c15:c18:null_MARK -> c7:c8:c9:null_A__X a__x :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark c8 :: c2:c3:c4:null_A__PLUS -> c7:c8:c9:null_A__X -> c11:c12:c13:c14:c15:c18:null_MARK -> c7:c8:c9:null_A__X c9 :: c2:c3:c4:null_A__PLUS -> c11:c12:c13:c14:c15:c18:null_MARK -> c7:c8:c9:null_A__X and :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark c11 :: c:null_A__AND -> c11:c12:c13:c14:c15:c18:null_MARK -> c11:c12:c13:c14:c15:c18:null_MARK plus :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark c12 :: c2:c3:c4:null_A__PLUS -> c11:c12:c13:c14:c15:c18:null_MARK -> c11:c12:c13:c14:c15:c18:null_MARK c13 :: c2:c3:c4:null_A__PLUS -> c11:c12:c13:c14:c15:c18:null_MARK -> c11:c12:c13:c14:c15:c18:null_MARK x :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark c14 :: c7:c8:c9:null_A__X -> c11:c12:c13:c14:c15:c18:null_MARK -> c11:c12:c13:c14:c15:c18:null_MARK c15 :: c7:c8:c9:null_A__X -> c11:c12:c13:c14:c15:c18:null_MARK -> c11:c12:c13:c14:c15:c18:null_MARK c18 :: c11:c12:c13:c14:c15:c18:null_MARK -> c11:c12:c13:c14:c15:c18:null_MARK a__and :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark a__plus :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark -> tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark null_a__and :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark null_a__plus :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark null_a__x :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark null_mark :: tt:0:s:and:plus:x:null_a__and:null_a__plus:null_a__x:null_mark null_A__AND :: c:null_A__AND null_A__PLUS :: c2:c3:c4:null_A__PLUS null_A__X :: c7:c8:c9:null_A__X null_MARK :: c11:c12:c13:c14:c15:c18:null_MARK Rewrite Strategy: INNERMOST ---------------------------------------- (73) 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_a__x => 0 null_mark => 0 null_A__AND => 0 null_A__PLUS => 0 null_A__X => 0 null_MARK => 0 ---------------------------------------- (74) 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 A__X(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__X(z, z') -{ 1 }-> 1 + A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)) + MARK(z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 A__X(z, z') -{ 1 }-> 1 + A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)) + A__X(mark(z0), mark(z1)) + MARK(z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 A__X(z, z') -{ 1 }-> 1 + A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)) + A__X(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__X(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__X(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__AND(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__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 a__x(z, z') -{ 0 }-> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 a__x(z, z') -{ 0 }-> 0 :|: z = z0, z0 >= 0, z' = 0 a__x(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__x(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 mark(z) -{ 0 }-> a__x(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 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. ---------------------------------------- (75) 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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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))) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) A__X(z0, s(z1)) -> c7(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z0)) A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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)) A__X(z0, s(z1)) -> c7(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z0)) A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, A__X_2, MARK_1 Compound Symbols: c_1, c2_1, c4_2, c7_3, c8_3, c9_2, c11_2, c12_2, c13_2, c14_2, c15_2, c18_1, c3_2 ---------------------------------------- (77) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) A__X(z0, s(z1)) -> c7(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z0)) A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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)) A__X(z0, s(z1)) -> c7(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z0)) A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, A__X_2, MARK_1 Compound Symbols: c_1, c2_1, c4_2, c7_3, c8_3, c9_2, c11_2, c12_2, c13_2, c14_2, c15_2, c18_1, c3_2, c3_1 ---------------------------------------- (79) 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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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__X(z0, s(z1)) -> c7(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z0)) A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(z0, s(z1)) -> c7(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z0)) A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, A__X_2, MARK_1 Compound Symbols: c_1, c2_1, c7_3, c8_3, c9_2, c11_2, c12_2, c13_2, c14_2, c15_2, c18_1, c3_2, c3_1, c4_2 ---------------------------------------- (81) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__PLUS(x0, s(tt)) -> c4(A__PLUS(mark(x0), tt), MARK(tt)) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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__X(z0, s(z1)) -> c7(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z0)) A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(z0, s(z1)) -> c7(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z0)) A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, A__X_2, MARK_1 Compound Symbols: c_1, c2_1, c7_3, c8_3, c9_2, c11_2, c12_2, c13_2, c14_2, c15_2, c18_1, c3_2, c3_1, c4_2 ---------------------------------------- (83) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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__X(z0, s(z1)) -> c7(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z0)) A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(z0, s(z1)) -> c7(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z0)) A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, A__X_2, MARK_1 Compound Symbols: c_1, c2_1, c7_3, c8_3, c9_2, c11_2, c12_2, c13_2, c14_2, c15_2, c18_1, c3_2, c3_1, c4_2, c4_1 ---------------------------------------- (85) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__X(z0, s(z1)) -> c7(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z0)) by A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(mark(tt), mark(x1)), tt), A__X(mark(tt), mark(x1)), MARK(tt)) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(0)) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(tt)) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(0)) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), 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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(mark(tt), mark(x1)), tt), A__X(mark(tt), mark(x1)), MARK(tt)) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(0)) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(tt)) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(0)) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(mark(tt), mark(x1)), tt), A__X(mark(tt), mark(x1)), MARK(tt)) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(0)) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(tt)) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(0)) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, A__X_2, MARK_1 Compound Symbols: c_1, c2_1, c8_3, c9_2, c11_2, c12_2, c13_2, c14_2, c15_2, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3 ---------------------------------------- (87) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, A__X_2, MARK_1 Compound Symbols: c_1, c2_1, c8_3, c9_2, c11_2, c12_2, c13_2, c14_2, c15_2, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2 ---------------------------------------- (89) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__X(z0, s(z1)) -> c8(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), A__X(mark(z0), mark(z1)), MARK(z1)) by A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(mark(tt), mark(x1)), tt), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(tt)) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(0)) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(mark(tt), mark(x1)), tt), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(tt)) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(0)) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(mark(tt), mark(x1)), tt), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(tt)) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(0)) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, A__X_2, MARK_1 Compound Symbols: c_1, c2_1, c9_2, c11_2, c12_2, c13_2, c14_2, c15_2, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3 ---------------------------------------- (91) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, A__X_2, MARK_1 Compound Symbols: c_1, c2_1, c9_2, c11_2, c12_2, c13_2, c14_2, c15_2, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2 ---------------------------------------- (93) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__X(z0, s(z1)) -> c9(A__PLUS(a__x(mark(z0), mark(z1)), mark(z0)), MARK(z0)) by A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(mark(tt), mark(x1)), tt), MARK(tt)) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0), MARK(0)) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt)), MARK(tt)) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0)), MARK(0)) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(mark(tt), mark(x1)), tt), MARK(tt)) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0), MARK(0)) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt)), MARK(tt)) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0)), MARK(0)) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(mark(tt), mark(x1)), tt), MARK(tt)) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0), MARK(0)) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt)), MARK(tt)) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0)), MARK(0)) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c11_2, c12_2, c13_2, c14_2, c15_2, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2 ---------------------------------------- (95) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__X(tt, s(x1)) -> c9(A__PLUS(a__x(mark(tt), mark(x1)), tt), MARK(tt)) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0), MARK(0)) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt)), MARK(tt)) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0)), MARK(0)) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0), MARK(0)) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt)), MARK(tt)) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0)), MARK(0)) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c11_2, c12_2, c13_2, c14_2, c15_2, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2 ---------------------------------------- (97) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c11_2, c12_2, c13_2, c14_2, c15_2, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1 ---------------------------------------- (99) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(and(z0, z1)) -> c11(A__AND(mark(z0), z1), MARK(z0)) by MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1), MARK(tt)) MARK(and(0, x1)) -> c11(A__AND(0, x1), MARK(0)) MARK(and(s(z0), x1)) -> c11(A__AND(s(mark(z0)), x1), MARK(s(z0))) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1), MARK(tt)) MARK(and(0, x1)) -> c11(A__AND(0, x1), MARK(0)) MARK(and(s(z0), x1)) -> c11(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)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1), MARK(tt)) MARK(and(0, x1)) -> c11(A__AND(0, x1), MARK(0)) MARK(and(s(z0), x1)) -> c11(A__AND(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c12_2, c13_2, c14_2, c15_2, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2 ---------------------------------------- (101) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(and(0, x1)) -> c11(A__AND(0, x1), MARK(0)) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c11(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)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1), MARK(tt)) MARK(and(s(z0), x1)) -> c11(A__AND(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c12_2, c13_2, c14_2, c15_2, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2 ---------------------------------------- (103) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c12_2, c13_2, c14_2, c15_2, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1 ---------------------------------------- (105) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(z0, z1)) -> c12(A__PLUS(mark(z0), mark(z1)), MARK(z0)) by MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, tt)) -> c12(A__PLUS(mark(x0), tt), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1)), MARK(tt)) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1)), MARK(0)) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, tt)) -> c12(A__PLUS(mark(x0), tt), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1)), MARK(tt)) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1)), MARK(0)) MARK(plus(s(z0), x1)) -> c12(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)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, tt)) -> c12(A__PLUS(mark(x0), tt), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1)), MARK(tt)) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1)), MARK(0)) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c13_2, c14_2, c15_2, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2 ---------------------------------------- (107) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(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)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c13_2, c14_2, c15_2, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1 ---------------------------------------- (109) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(z0, z1)) -> c13(A__PLUS(mark(z0), mark(z1)), MARK(z1)) by MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, tt)) -> c13(A__PLUS(mark(x0), tt), MARK(tt)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, tt)) -> c13(A__PLUS(mark(x0), tt), MARK(tt)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(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(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, tt)) -> c13(A__PLUS(mark(x0), tt), MARK(tt)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c14_2, c15_2, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2 ---------------------------------------- (111) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(x0, tt)) -> c13(A__PLUS(mark(x0), tt), MARK(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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(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(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c14_2, c15_2, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2 ---------------------------------------- (113) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c14_2, c15_2, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1 ---------------------------------------- (115) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(x(z0, z1)) -> c14(A__X(mark(z0), mark(z1)), MARK(z0)) by MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, tt)) -> c14(A__X(mark(x0), tt), MARK(x0)) MARK(x(x0, 0)) -> c14(A__X(mark(x0), 0), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1)), MARK(tt)) MARK(x(0, x1)) -> c14(A__X(0, mark(x1)), MARK(0)) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, tt)) -> c14(A__X(mark(x0), tt), MARK(x0)) MARK(x(x0, 0)) -> c14(A__X(mark(x0), 0), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1)), MARK(tt)) MARK(x(0, x1)) -> c14(A__X(0, mark(x1)), MARK(0)) MARK(x(s(z0), x1)) -> c14(A__X(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(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, tt)) -> c14(A__X(mark(x0), tt), MARK(x0)) MARK(x(x0, 0)) -> c14(A__X(mark(x0), 0), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1)), MARK(tt)) MARK(x(0, x1)) -> c14(A__X(0, mark(x1)), MARK(0)) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c15_2, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2 ---------------------------------------- (117) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c15_2, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1 ---------------------------------------- (119) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(x(z0, z1)) -> c15(A__X(mark(z0), mark(z1)), MARK(z1)) by MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, tt)) -> c15(A__X(mark(x0), tt), MARK(tt)) MARK(x(x0, 0)) -> c15(A__X(mark(x0), 0), MARK(0)) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, tt)) -> c15(A__X(mark(x0), tt), MARK(tt)) MARK(x(x0, 0)) -> c15(A__X(mark(x0), 0), MARK(0)) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(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)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, tt)) -> c15(A__X(mark(x0), tt), MARK(tt)) MARK(x(x0, 0)) -> c15(A__X(mark(x0), 0), MARK(0)) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (121) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(x(x0, 0)) -> c15(A__X(mark(x0), 0), MARK(0)) MARK(x(x0, tt)) -> c15(A__X(mark(x0), tt), MARK(tt)) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(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)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (123) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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))) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (125) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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)) -> c18(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(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (127) 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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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))) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(MARK(z0)) A__PLUS(x0, s(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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)) -> c18(MARK(z0)) A__PLUS(x0, s(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (129) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(MARK(z0)) A__PLUS(x0, s(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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)) -> c18(MARK(z0)) A__PLUS(x0, s(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (131) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(x0, s(x(z0, z1))) -> c3(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) by A__PLUS(x0, s(x(x1, x2))) -> c3(A__PLUS(mark(x0), x(mark(x1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(tt)) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(0)) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, x2))) -> c3(A__PLUS(mark(x0), x(mark(x1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(tt)) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(0)) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(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)) -> c18(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, x2))) -> c3(A__PLUS(mark(x0), x(mark(x1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(tt)) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(0)) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (133) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(mark(x1), mark(x2)))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c18(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), 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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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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)) 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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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(mark(x1), mark(x2)))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (135) 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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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))) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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)) -> c18(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), 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A__PLUS(0, s(plus(x1, x2))) -> c3(A__PLUS(0, a__plus(mark(x1), mark(x2)))) A__PLUS(x0, s(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (137) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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)) -> c18(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) 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A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (139) 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(x(z0, z1))) -> c3(A__PLUS(a__and(mark(x0), x1), a__x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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))) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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)) -> c18(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, 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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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (141) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), 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MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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)) -> c18(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(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (143) 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(x(z0, z1))) -> c3(A__PLUS(a__plus(mark(x0), mark(x1)), a__x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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))) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), 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c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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)) -> c18(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) 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a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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), 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mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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)) -> c18(MARK(z0)) A__PLUS(x0, s(0)) -> c3(A__PLUS(mark(x0), 0), MARK(x0)) A__PLUS(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), 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MARK(x0)) A__PLUS(x0, s(plus(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (147) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(x(z0, z1), s(x1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) by A__PLUS(x(x0, x1), s(and(z0, z1))) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), a__and(mark(z0), z1)), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(plus(z0, z1))) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x(z0, z1))) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), tt), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(s(z0))) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), s(mark(z0))), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), 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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, 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c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(tt)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), tt), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), 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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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(tt)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), tt), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (149) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), 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s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(x0, x1))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c18(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(x0, x1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (151) 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(x(z0, z1))) -> c3(A__PLUS(s(mark(x0)), a__x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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))) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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)) -> c18(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), 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MARK(x0)) A__PLUS(x0, s(plus(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (153) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), 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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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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)) -> c18(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, 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c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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)), 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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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (155) 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(x(z0, z1))) -> c3(A__PLUS(tt, a__x(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)))) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> 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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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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))) 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c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, 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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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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)) -> c18(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), 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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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (157) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__PLUS(tt, s(tt)) -> c3(A__PLUS(tt, tt)) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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)) -> c18(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (159) 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(x(z0, z1))) -> c3(A__PLUS(0, a__x(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)))) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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)) -> c18(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> 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MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> 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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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, 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mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(plus(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (161) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__PLUS(0, s(tt)) -> c3(A__PLUS(0, tt)) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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)) -> c18(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (163) 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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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))) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 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c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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)) -> c18(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (165) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> 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MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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)) -> c18(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), 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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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (167) 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, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(plus(x1, x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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))) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, 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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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(plus(x1, x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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)) -> c18(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> 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a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(plus(x1, x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (169) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(plus(x1, x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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)) -> c18(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(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), 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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, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(plus(x1, x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (171) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(x0, s(x(z0, z1))) -> c4(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) by A__PLUS(x0, s(x(x1, x2))) -> c4(A__PLUS(mark(x0), x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(plus(x1, x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, x2))) -> c4(A__PLUS(mark(x0), x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c18(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) 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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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(plus(x1, x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, x2))) -> c4(A__PLUS(mark(x0), x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (173) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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))) 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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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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, 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-> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(x1, x2))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c18(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, 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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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), 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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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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))) 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A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(plus(x1, x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(x1, x2))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (175) 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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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))) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), 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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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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), 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MARK(plus(plus(z0, z1), x1))) A__PLUS(plus(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(plus(x1, x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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)) -> c18(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(z0, z1))) A__PLUS(s(z0), 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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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(tt, s(plus(x1, x2))) -> 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s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (177) 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(x(z0, z1))) -> c4(A__PLUS(a__and(mark(x0), x1), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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)) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), 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c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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), 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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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), 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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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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)) -> c18(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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), 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a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (179) 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)) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), 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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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(plus(x1, x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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)) -> c18(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(plus(x1, x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (181) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(plus(x1, x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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)) -> c18(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), 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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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(plus(x1, x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (183) 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(x(z0, z1))) -> c4(A__PLUS(a__plus(mark(x0), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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)) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(plus(x1, x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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)) -> c18(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, 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c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) 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c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (185) 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)) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), 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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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(plus(x1, x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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)) -> c18(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), 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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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (187) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) 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MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(plus(x1, x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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)) -> c18(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(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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, 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mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, 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s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(plus(x1, x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (189) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(x(z0, z1), s(x1)) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) by A__PLUS(x(x0, x1), s(and(z0, z1))) -> c4(A__PLUS(a__x(mark(x0), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__PLUS(x(x0, x1), s(plus(z0, z1))) -> c4(A__PLUS(a__x(mark(x0), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__PLUS(x(x0, x1), s(x(z0, z1))) -> c4(A__PLUS(a__x(mark(x0), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__PLUS(x(x0, x1), s(tt)) -> c4(A__PLUS(a__x(mark(x0), mark(x1)), tt), MARK(tt)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(0)) A__PLUS(x(x0, x1), s(s(z0))) -> c4(A__PLUS(a__x(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) A__PLUS(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(plus(x1, x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(tt)) -> c4(A__PLUS(a__x(mark(x0), mark(x1)), tt), MARK(tt)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(0)) A__PLUS(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(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)) -> c18(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), 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s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(plus(x1, x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(tt)) -> c4(A__PLUS(a__x(mark(x0), mark(x1)), tt), MARK(tt)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(0)) A__PLUS(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (191) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__PLUS(x(x0, x1), s(tt)) -> c4(A__PLUS(a__x(mark(x0), mark(x1)), tt), MARK(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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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)), 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z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(0)) A__PLUS(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(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)) -> c18(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), 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c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, 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a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(x0)) A__PLUS(x0, s(and(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, 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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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, 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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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(plus(x1, x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(0)) A__PLUS(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (193) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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, 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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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), 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a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(mark(x0), mark(x1)), 0)) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c18(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), 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A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) 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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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(mark(x0), mark(x1)), 0)) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (195) 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(x(z0, z1))) -> c4(A__PLUS(tt, a__x(mark(z0), mark(z1))), MARK(x(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))) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) 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A__PLUS(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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)) -> c18(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(plus(x1, x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (197) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__PLUS(tt, s(tt)) -> c4(A__PLUS(tt, tt), MARK(tt)) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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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MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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)) -> c18(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, 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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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) A__PLUS(x0, 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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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), 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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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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))) 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A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(plus(x1, x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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)) -> c18(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> 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c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (201) 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(x(z0, z1))) -> c4(A__PLUS(0, a__x(mark(z0), mark(z1))), MARK(x(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))) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, 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MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(plus(x1, x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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)) -> c18(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(plus(x1, x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (203) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__PLUS(0, s(tt)) -> c4(A__PLUS(0, tt), MARK(tt)) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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)), 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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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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)) -> c18(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) 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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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (205) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, 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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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, 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s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(x0, 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MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(plus(x1, x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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)) -> c18(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> 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MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_2, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2 ---------------------------------------- (207) 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(x(z0, z1))) -> c4(A__PLUS(s(mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) 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MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) -> c18(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(plus(x1, x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c4_2 ---------------------------------------- (209) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__PLUS(s(x0), s(tt)) -> c4(A__PLUS(s(mark(x0)), tt), MARK(tt)) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), 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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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) -> c18(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> 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mark(x2)), MARK(x2)) A__PLUS(plus(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c4_2 ---------------------------------------- (211) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) 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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, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(plus(x1, x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) -> c18(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> 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MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> 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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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, 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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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c4_2 ---------------------------------------- (213) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) by A__X(and(x0, z1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x0, z1)), mark(x2)), and(mark(x0), z1)), A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2)), MARK(and(0, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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)) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) 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mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), 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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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(x0, z1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x0, z1)), mark(x2)), and(mark(x0), z1)), A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2)), MARK(and(0, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c18(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)) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), 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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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(x0, z1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x0, z1)), mark(x2)), and(mark(x0), z1)), A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2)), MARK(and(0, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c4_2 ---------------------------------------- (215) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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)) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> 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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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c18(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)) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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)) -> 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MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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, 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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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c4_2 ---------------------------------------- (217) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) by A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), mark(x2)), plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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)) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 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c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, 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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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, 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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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(plus(x1, x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), mark(x2)), plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c18(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)) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), 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mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), mark(x2)), plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c4_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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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)) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(plus(x1, 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MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), 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c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c18(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)) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> 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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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c4_2 ---------------------------------------- (221) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) by A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), mark(x2)), x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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)) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> 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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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), mark(x2)), x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c18(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)) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(plus(x1, x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), mark(x2)), x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c4_2 ---------------------------------------- (223) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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)) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> 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mark(x2)), MARK(x2)) A__PLUS(plus(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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)), 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MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) A__X(x(x0, x1), s(x2)) -> c7(A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c18(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)) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(plus(x1, tt))) -> c3(A__PLUS(mark(x0), 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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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> 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mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) A__X(x(x0, x1), s(x2)) -> c7(A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c4_2 ---------------------------------------- (225) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) by A__X(s(s(z0)), s(x1)) -> c7(A__PLUS(a__x(mark(s(s(z0))), mark(x1)), s(s(mark(z0)))), A__X(mark(s(s(z0))), mark(x1)), MARK(s(s(z0)))) A__X(s(and(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(and(z0, z1))), mark(x1)), s(a__and(mark(z0), z1))), A__X(mark(s(and(z0, z1))), mark(x1)), MARK(s(and(z0, z1)))) A__X(s(plus(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(plus(z0, z1))), mark(x1)), s(a__plus(mark(z0), mark(z1)))), A__X(mark(s(plus(z0, z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__X(s(x(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(x(z0, z1))), mark(x1)), s(a__x(mark(z0), mark(z1)))), A__X(mark(s(x(z0, z1))), mark(x1)), MARK(s(x(z0, z1)))) A__X(s(tt), s(x1)) -> c7(A__PLUS(a__x(mark(s(tt)), mark(x1)), s(tt)), A__X(mark(s(tt)), mark(x1)), MARK(s(tt))) A__X(s(0), s(x1)) -> c7(A__PLUS(a__x(mark(s(0)), mark(x1)), s(0)), A__X(mark(s(0)), mark(x1)), MARK(s(0))) A__X(s(x0), s(x1)) -> c7(A__PLUS(x(mark(s(x0)), mark(x1)), s(mark(x0))), A__X(mark(s(x0)), mark(x1)), MARK(s(x0))) A__X(s(x0), s(s(z0))) -> c7(A__PLUS(a__x(mark(s(x0)), s(mark(z0))), s(mark(x0))), A__X(mark(s(x0)), mark(s(z0))), MARK(s(x0))) A__X(s(x0), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__and(mark(z0), z1)), s(mark(x0))), A__X(mark(s(x0)), mark(and(z0, z1))), MARK(s(x0))) A__X(s(x0), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__plus(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(plus(z0, z1))), MARK(s(x0))) A__X(s(x0), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__x(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(x(z0, z1))), MARK(s(x0))) A__X(s(x0), s(tt)) -> c7(A__PLUS(a__x(mark(s(x0)), tt), s(mark(x0))), A__X(mark(s(x0)), mark(tt)), MARK(s(x0))) A__X(s(x0), s(0)) -> c7(A__PLUS(a__x(mark(s(x0)), 0), s(mark(x0))), A__X(mark(s(x0)), mark(0)), MARK(s(x0))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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)) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> 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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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) A__X(x(x0, x1), s(x2)) -> c7(A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(s(s(z0)), s(x1)) -> c7(A__PLUS(a__x(mark(s(s(z0))), mark(x1)), s(s(mark(z0)))), A__X(mark(s(s(z0))), mark(x1)), MARK(s(s(z0)))) A__X(s(and(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(and(z0, z1))), mark(x1)), s(a__and(mark(z0), z1))), A__X(mark(s(and(z0, z1))), mark(x1)), MARK(s(and(z0, z1)))) A__X(s(plus(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(plus(z0, z1))), mark(x1)), s(a__plus(mark(z0), mark(z1)))), A__X(mark(s(plus(z0, z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__X(s(x(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(x(z0, z1))), mark(x1)), s(a__x(mark(z0), mark(z1)))), A__X(mark(s(x(z0, z1))), mark(x1)), MARK(s(x(z0, z1)))) A__X(s(tt), s(x1)) -> c7(A__PLUS(a__x(mark(s(tt)), mark(x1)), s(tt)), A__X(mark(s(tt)), mark(x1)), MARK(s(tt))) A__X(s(0), s(x1)) -> c7(A__PLUS(a__x(mark(s(0)), mark(x1)), s(0)), A__X(mark(s(0)), mark(x1)), MARK(s(0))) A__X(s(x0), s(x1)) -> c7(A__PLUS(x(mark(s(x0)), mark(x1)), s(mark(x0))), A__X(mark(s(x0)), mark(x1)), MARK(s(x0))) A__X(s(x0), s(s(z0))) -> c7(A__PLUS(a__x(mark(s(x0)), s(mark(z0))), s(mark(x0))), A__X(mark(s(x0)), mark(s(z0))), MARK(s(x0))) A__X(s(x0), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__and(mark(z0), z1)), s(mark(x0))), A__X(mark(s(x0)), mark(and(z0, z1))), MARK(s(x0))) A__X(s(x0), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__plus(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(plus(z0, z1))), MARK(s(x0))) A__X(s(x0), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__x(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(x(z0, z1))), MARK(s(x0))) A__X(s(x0), s(tt)) -> c7(A__PLUS(a__x(mark(s(x0)), tt), s(mark(x0))), A__X(mark(s(x0)), mark(tt)), MARK(s(x0))) A__X(s(x0), s(0)) -> c7(A__PLUS(a__x(mark(s(x0)), 0), s(mark(x0))), A__X(mark(s(x0)), mark(0)), MARK(s(x0))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c18(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)) A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, 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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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) A__X(x(x0, x1), s(x2)) -> c7(A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(s(s(z0)), s(x1)) -> c7(A__PLUS(a__x(mark(s(s(z0))), mark(x1)), s(s(mark(z0)))), A__X(mark(s(s(z0))), mark(x1)), MARK(s(s(z0)))) A__X(s(and(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(and(z0, z1))), mark(x1)), s(a__and(mark(z0), z1))), A__X(mark(s(and(z0, z1))), mark(x1)), MARK(s(and(z0, z1)))) A__X(s(plus(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(plus(z0, z1))), mark(x1)), s(a__plus(mark(z0), mark(z1)))), A__X(mark(s(plus(z0, z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__X(s(x(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(x(z0, z1))), mark(x1)), s(a__x(mark(z0), mark(z1)))), A__X(mark(s(x(z0, z1))), mark(x1)), MARK(s(x(z0, z1)))) A__X(s(tt), s(x1)) -> c7(A__PLUS(a__x(mark(s(tt)), mark(x1)), s(tt)), A__X(mark(s(tt)), mark(x1)), MARK(s(tt))) A__X(s(0), s(x1)) -> c7(A__PLUS(a__x(mark(s(0)), mark(x1)), s(0)), A__X(mark(s(0)), mark(x1)), MARK(s(0))) A__X(s(x0), s(x1)) -> c7(A__PLUS(x(mark(s(x0)), mark(x1)), s(mark(x0))), A__X(mark(s(x0)), mark(x1)), MARK(s(x0))) A__X(s(x0), s(s(z0))) -> c7(A__PLUS(a__x(mark(s(x0)), s(mark(z0))), s(mark(x0))), A__X(mark(s(x0)), mark(s(z0))), MARK(s(x0))) A__X(s(x0), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__and(mark(z0), z1)), s(mark(x0))), A__X(mark(s(x0)), mark(and(z0, z1))), MARK(s(x0))) A__X(s(x0), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__plus(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(plus(z0, z1))), MARK(s(x0))) A__X(s(x0), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__x(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(x(z0, z1))), MARK(s(x0))) A__X(s(x0), s(tt)) -> c7(A__PLUS(a__x(mark(s(x0)), tt), s(mark(x0))), A__X(mark(s(x0)), mark(tt)), MARK(s(x0))) A__X(s(x0), s(0)) -> c7(A__PLUS(a__x(mark(s(x0)), 0), s(mark(x0))), A__X(mark(s(x0)), mark(0)), MARK(s(x0))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c4_2 ---------------------------------------- (227) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__X(x0, s(x1)) -> c7(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x0)) by A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(tt, s(x1)) -> c7(A__PLUS(x(mark(tt), mark(x1)), tt), A__X(mark(tt), mark(x1)), MARK(tt)) A__X(0, s(x1)) -> c7(A__PLUS(x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(0)) A__X(s(z0), s(x1)) -> c7(A__PLUS(x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(tt, s(x1)) -> c7(A__PLUS(x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(tt)) A__X(0, s(x1)) -> c7(A__PLUS(x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(0)) A__X(s(z0), s(x1)) -> c7(A__PLUS(x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) 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mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) A__X(x(x0, x1), s(x2)) -> c7(A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(s(s(z0)), s(x1)) -> c7(A__PLUS(a__x(mark(s(s(z0))), mark(x1)), s(s(mark(z0)))), A__X(mark(s(s(z0))), mark(x1)), MARK(s(s(z0)))) A__X(s(and(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(and(z0, z1))), mark(x1)), s(a__and(mark(z0), z1))), A__X(mark(s(and(z0, z1))), mark(x1)), MARK(s(and(z0, z1)))) A__X(s(plus(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(plus(z0, z1))), mark(x1)), s(a__plus(mark(z0), mark(z1)))), A__X(mark(s(plus(z0, z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__X(s(x(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(x(z0, z1))), mark(x1)), s(a__x(mark(z0), mark(z1)))), A__X(mark(s(x(z0, z1))), mark(x1)), MARK(s(x(z0, z1)))) A__X(s(tt), s(x1)) -> c7(A__PLUS(a__x(mark(s(tt)), mark(x1)), s(tt)), A__X(mark(s(tt)), mark(x1)), MARK(s(tt))) A__X(s(0), s(x1)) -> c7(A__PLUS(a__x(mark(s(0)), mark(x1)), s(0)), A__X(mark(s(0)), mark(x1)), MARK(s(0))) A__X(s(x0), s(x1)) -> c7(A__PLUS(x(mark(s(x0)), mark(x1)), s(mark(x0))), A__X(mark(s(x0)), mark(x1)), MARK(s(x0))) A__X(s(x0), s(s(z0))) -> c7(A__PLUS(a__x(mark(s(x0)), s(mark(z0))), s(mark(x0))), A__X(mark(s(x0)), mark(s(z0))), MARK(s(x0))) A__X(s(x0), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__and(mark(z0), z1)), s(mark(x0))), A__X(mark(s(x0)), mark(and(z0, z1))), MARK(s(x0))) A__X(s(x0), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__plus(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(plus(z0, z1))), MARK(s(x0))) A__X(s(x0), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__x(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(x(z0, z1))), MARK(s(x0))) A__X(s(x0), s(tt)) -> c7(A__PLUS(a__x(mark(s(x0)), tt), s(mark(x0))), A__X(mark(s(x0)), mark(tt)), MARK(s(x0))) A__X(s(x0), s(0)) -> c7(A__PLUS(a__x(mark(s(x0)), 0), s(mark(x0))), A__X(mark(s(x0)), mark(0)), MARK(s(x0))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__PLUS(x(mark(tt), mark(x1)), tt), A__X(mark(tt), mark(x1)), MARK(tt)) A__X(0, s(x1)) -> c7(A__PLUS(x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(tt, s(x1)) -> c7(A__PLUS(x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(tt)) A__X(0, s(x1)) -> c7(A__PLUS(x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(0)) A__X(s(z0), s(x1)) -> c7(A__PLUS(x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c18(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)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), 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x1), mark(x2)), MARK(and(plus(z0, z1), x1))) A__PLUS(and(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(plus(x1, x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) A__X(x(x0, x1), s(x2)) -> c7(A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(s(s(z0)), s(x1)) -> c7(A__PLUS(a__x(mark(s(s(z0))), mark(x1)), s(s(mark(z0)))), A__X(mark(s(s(z0))), mark(x1)), MARK(s(s(z0)))) A__X(s(and(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(and(z0, z1))), mark(x1)), s(a__and(mark(z0), z1))), A__X(mark(s(and(z0, z1))), mark(x1)), MARK(s(and(z0, z1)))) A__X(s(plus(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(plus(z0, z1))), mark(x1)), s(a__plus(mark(z0), mark(z1)))), A__X(mark(s(plus(z0, z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__X(s(x(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(x(z0, z1))), mark(x1)), s(a__x(mark(z0), mark(z1)))), A__X(mark(s(x(z0, z1))), mark(x1)), MARK(s(x(z0, z1)))) A__X(s(tt), s(x1)) -> c7(A__PLUS(a__x(mark(s(tt)), mark(x1)), s(tt)), A__X(mark(s(tt)), mark(x1)), MARK(s(tt))) A__X(s(0), s(x1)) -> c7(A__PLUS(a__x(mark(s(0)), mark(x1)), s(0)), A__X(mark(s(0)), mark(x1)), MARK(s(0))) A__X(s(x0), s(x1)) -> c7(A__PLUS(x(mark(s(x0)), mark(x1)), s(mark(x0))), A__X(mark(s(x0)), mark(x1)), MARK(s(x0))) A__X(s(x0), s(s(z0))) -> c7(A__PLUS(a__x(mark(s(x0)), s(mark(z0))), s(mark(x0))), A__X(mark(s(x0)), mark(s(z0))), MARK(s(x0))) A__X(s(x0), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__and(mark(z0), z1)), s(mark(x0))), A__X(mark(s(x0)), mark(and(z0, z1))), MARK(s(x0))) A__X(s(x0), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__plus(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(plus(z0, z1))), MARK(s(x0))) A__X(s(x0), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__x(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(x(z0, z1))), MARK(s(x0))) A__X(s(x0), s(tt)) -> c7(A__PLUS(a__x(mark(s(x0)), tt), s(mark(x0))), A__X(mark(s(x0)), mark(tt)), MARK(s(x0))) A__X(s(x0), s(0)) -> c7(A__PLUS(a__x(mark(s(x0)), 0), s(mark(x0))), A__X(mark(s(x0)), mark(0)), MARK(s(x0))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__PLUS(x(mark(tt), mark(x1)), tt), A__X(mark(tt), mark(x1)), MARK(tt)) A__X(0, s(x1)) -> c7(A__PLUS(x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(0)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(tt, s(x1)) -> c7(A__PLUS(x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(tt)) A__X(0, s(x1)) -> c7(A__PLUS(x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(0)) A__X(s(z0), s(x1)) -> c7(A__PLUS(x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c4_2 ---------------------------------------- (229) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> 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c3(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__PLUS(s(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(plus(x1, x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) A__X(x(x0, x1), s(x2)) -> c7(A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(s(s(z0)), s(x1)) -> c7(A__PLUS(a__x(mark(s(s(z0))), mark(x1)), s(s(mark(z0)))), A__X(mark(s(s(z0))), mark(x1)), MARK(s(s(z0)))) A__X(s(and(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(and(z0, z1))), mark(x1)), s(a__and(mark(z0), z1))), A__X(mark(s(and(z0, z1))), mark(x1)), MARK(s(and(z0, z1)))) A__X(s(plus(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(plus(z0, z1))), mark(x1)), s(a__plus(mark(z0), mark(z1)))), A__X(mark(s(plus(z0, z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__X(s(x(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(x(z0, z1))), mark(x1)), s(a__x(mark(z0), mark(z1)))), A__X(mark(s(x(z0, z1))), mark(x1)), MARK(s(x(z0, z1)))) A__X(s(tt), s(x1)) -> c7(A__PLUS(a__x(mark(s(tt)), mark(x1)), s(tt)), A__X(mark(s(tt)), mark(x1)), MARK(s(tt))) A__X(s(0), s(x1)) -> c7(A__PLUS(a__x(mark(s(0)), mark(x1)), s(0)), A__X(mark(s(0)), mark(x1)), MARK(s(0))) A__X(s(x0), s(x1)) -> c7(A__PLUS(x(mark(s(x0)), mark(x1)), s(mark(x0))), A__X(mark(s(x0)), mark(x1)), MARK(s(x0))) A__X(s(x0), s(s(z0))) -> c7(A__PLUS(a__x(mark(s(x0)), s(mark(z0))), s(mark(x0))), A__X(mark(s(x0)), mark(s(z0))), MARK(s(x0))) A__X(s(x0), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__and(mark(z0), z1)), s(mark(x0))), A__X(mark(s(x0)), mark(and(z0, z1))), MARK(s(x0))) A__X(s(x0), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__plus(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(plus(z0, z1))), MARK(s(x0))) A__X(s(x0), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__x(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(x(z0, z1))), MARK(s(x0))) A__X(s(x0), s(tt)) -> c7(A__PLUS(a__x(mark(s(x0)), tt), s(mark(x0))), A__X(mark(s(x0)), mark(tt)), MARK(s(x0))) A__X(s(x0), s(0)) -> c7(A__PLUS(a__x(mark(s(x0)), 0), s(mark(x0))), A__X(mark(s(x0)), mark(0)), MARK(s(x0))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(0, s(x1)) -> c7(A__PLUS(x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c18(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)) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> 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s(plus(x1, x2))) -> c4(MARK(plus(x1, x2))) A__PLUS(x0, s(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) A__X(x(x0, x1), s(x2)) -> c7(A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(s(s(z0)), s(x1)) -> c7(A__PLUS(a__x(mark(s(s(z0))), mark(x1)), s(s(mark(z0)))), A__X(mark(s(s(z0))), mark(x1)), MARK(s(s(z0)))) A__X(s(and(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(and(z0, z1))), mark(x1)), s(a__and(mark(z0), z1))), A__X(mark(s(and(z0, z1))), mark(x1)), MARK(s(and(z0, z1)))) A__X(s(plus(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(plus(z0, z1))), mark(x1)), s(a__plus(mark(z0), mark(z1)))), A__X(mark(s(plus(z0, z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__X(s(x(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(x(z0, z1))), mark(x1)), s(a__x(mark(z0), mark(z1)))), A__X(mark(s(x(z0, z1))), mark(x1)), MARK(s(x(z0, z1)))) A__X(s(tt), s(x1)) -> c7(A__PLUS(a__x(mark(s(tt)), mark(x1)), s(tt)), A__X(mark(s(tt)), mark(x1)), MARK(s(tt))) A__X(s(0), s(x1)) -> c7(A__PLUS(a__x(mark(s(0)), mark(x1)), s(0)), A__X(mark(s(0)), mark(x1)), MARK(s(0))) A__X(s(x0), s(x1)) -> c7(A__PLUS(x(mark(s(x0)), mark(x1)), s(mark(x0))), A__X(mark(s(x0)), mark(x1)), MARK(s(x0))) A__X(s(x0), s(s(z0))) -> c7(A__PLUS(a__x(mark(s(x0)), s(mark(z0))), s(mark(x0))), A__X(mark(s(x0)), mark(s(z0))), MARK(s(x0))) A__X(s(x0), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__and(mark(z0), z1)), s(mark(x0))), A__X(mark(s(x0)), mark(and(z0, z1))), MARK(s(x0))) A__X(s(x0), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__plus(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(plus(z0, z1))), MARK(s(x0))) A__X(s(x0), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__x(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(x(z0, z1))), MARK(s(x0))) A__X(s(x0), s(tt)) -> c7(A__PLUS(a__x(mark(s(x0)), tt), s(mark(x0))), A__X(mark(s(x0)), mark(tt)), MARK(s(x0))) A__X(s(x0), s(0)) -> c7(A__PLUS(a__x(mark(s(x0)), 0), s(mark(x0))), A__X(mark(s(x0)), mark(0)), MARK(s(x0))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(0, s(x1)) -> c7(A__PLUS(x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c4_2 ---------------------------------------- (231) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) by A__X(and(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(mark(and(z0, z1)), a__and(mark(x1), x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(and(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), a__and(mark(x1), x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(and(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(mark(x(z0, z1)), a__and(mark(x1), x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(and(x1, x2))), MARK(x(z0, z1))) A__X(tt, s(and(x1, x2))) -> c7(A__PLUS(a__x(mark(tt), a__and(mark(x1), x2)), tt), A__X(mark(tt), mark(and(x1, x2))), MARK(tt)) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__and(mark(x1), x2)), 0), A__X(mark(0), mark(and(x1, x2))), MARK(0)) A__X(s(z0), s(and(x1, x2))) -> c7(A__PLUS(a__x(mark(s(z0)), a__and(mark(x1), x2)), s(mark(z0))), A__X(mark(s(z0)), mark(and(x1, x2))), MARK(s(z0))) A__X(x0, s(and(x1, x2))) -> c7(A__PLUS(x(mark(x0), a__and(mark(x1), x2)), mark(x0)), A__X(mark(x0), mark(and(x1, x2))), MARK(x0)) A__X(x0, s(and(x1, z1))) -> c7(A__PLUS(a__x(mark(x0), and(mark(x1), z1)), mark(x0)), A__X(mark(x0), mark(and(x1, z1))), MARK(x0)) A__X(x0, s(and(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__and(mark(z0), z1), x2)), mark(x0)), A__X(mark(x0), mark(and(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(tt, x2)), mark(x0)), A__X(mark(x0), mark(and(tt, x2))), MARK(x0)) A__X(x0, s(and(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(0, x2)), mark(x0)), A__X(mark(x0), mark(and(0, x2))), MARK(x0)) A__X(x0, s(and(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(s(mark(z0)), x2)), mark(x0)), A__X(mark(x0), mark(and(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__and(mark(x1), x2)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(and(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(and(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(and(x1, x2))), MARK(x(z0, z1))) A__X(tt, s(and(x1, x2))) -> c7(A__PLUS(a__x(tt, a__and(mark(x1), x2)), mark(tt)), A__X(mark(tt), mark(and(x1, x2))), MARK(tt)) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(0, a__and(mark(x1), x2)), mark(0)), A__X(mark(0), mark(and(x1, x2))), MARK(0)) A__X(s(z0), s(and(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__and(mark(x1), x2)), mark(s(z0))), A__X(mark(s(z0)), mark(and(x1, x2))), MARK(s(z0))) A__X(x0, s(and(x1, x2))) -> c7(A__X(mark(x0), mark(and(x1, x2)))) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), 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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, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(plus(x1, x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) A__X(x(x0, x1), s(x2)) -> c7(A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(s(s(z0)), s(x1)) -> c7(A__PLUS(a__x(mark(s(s(z0))), mark(x1)), s(s(mark(z0)))), A__X(mark(s(s(z0))), mark(x1)), MARK(s(s(z0)))) A__X(s(and(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(and(z0, z1))), mark(x1)), s(a__and(mark(z0), z1))), A__X(mark(s(and(z0, z1))), mark(x1)), MARK(s(and(z0, z1)))) A__X(s(plus(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(plus(z0, z1))), mark(x1)), s(a__plus(mark(z0), mark(z1)))), A__X(mark(s(plus(z0, z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__X(s(x(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(x(z0, z1))), mark(x1)), s(a__x(mark(z0), mark(z1)))), A__X(mark(s(x(z0, z1))), mark(x1)), MARK(s(x(z0, z1)))) A__X(s(tt), s(x1)) -> c7(A__PLUS(a__x(mark(s(tt)), mark(x1)), s(tt)), A__X(mark(s(tt)), mark(x1)), MARK(s(tt))) A__X(s(0), s(x1)) -> c7(A__PLUS(a__x(mark(s(0)), mark(x1)), s(0)), A__X(mark(s(0)), mark(x1)), MARK(s(0))) A__X(s(x0), s(x1)) -> c7(A__PLUS(x(mark(s(x0)), mark(x1)), s(mark(x0))), A__X(mark(s(x0)), mark(x1)), MARK(s(x0))) A__X(s(x0), s(s(z0))) -> c7(A__PLUS(a__x(mark(s(x0)), s(mark(z0))), s(mark(x0))), A__X(mark(s(x0)), mark(s(z0))), MARK(s(x0))) A__X(s(x0), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__and(mark(z0), z1)), s(mark(x0))), A__X(mark(s(x0)), mark(and(z0, z1))), MARK(s(x0))) A__X(s(x0), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__plus(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(plus(z0, z1))), MARK(s(x0))) A__X(s(x0), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__x(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(x(z0, z1))), MARK(s(x0))) A__X(s(x0), s(tt)) -> c7(A__PLUS(a__x(mark(s(x0)), tt), s(mark(x0))), A__X(mark(s(x0)), mark(tt)), MARK(s(x0))) A__X(s(x0), s(0)) -> c7(A__PLUS(a__x(mark(s(x0)), 0), s(mark(x0))), A__X(mark(s(x0)), mark(0)), MARK(s(x0))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(0, s(x1)) -> c7(A__PLUS(x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(tt, s(and(x1, x2))) -> c7(A__PLUS(a__x(mark(tt), a__and(mark(x1), x2)), tt), A__X(mark(tt), mark(and(x1, x2))), MARK(tt)) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__and(mark(x1), x2)), 0), A__X(mark(0), mark(and(x1, x2))), MARK(0)) A__X(x0, s(and(x1, z1))) -> c7(A__PLUS(a__x(mark(x0), and(mark(x1), z1)), mark(x0)), A__X(mark(x0), mark(and(x1, z1))), MARK(x0)) A__X(x0, s(and(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__and(mark(z0), z1), x2)), mark(x0)), A__X(mark(x0), mark(and(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(tt, x2)), mark(x0)), A__X(mark(x0), mark(and(tt, x2))), MARK(x0)) A__X(x0, s(and(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(0, x2)), mark(x0)), A__X(mark(x0), mark(and(0, x2))), MARK(x0)) A__X(x0, s(and(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(s(mark(z0)), x2)), mark(x0)), A__X(mark(x0), mark(and(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__and(mark(x1), x2)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(and(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(and(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(and(x1, x2))), MARK(x(z0, z1))) A__X(tt, s(and(x1, x2))) -> c7(A__PLUS(a__x(tt, a__and(mark(x1), x2)), mark(tt)), A__X(mark(tt), mark(and(x1, x2))), MARK(tt)) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(0, a__and(mark(x1), x2)), mark(0)), A__X(mark(0), mark(and(x1, x2))), MARK(0)) A__X(s(z0), s(and(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__and(mark(x1), x2)), mark(s(z0))), A__X(mark(s(z0)), mark(and(x1, x2))), MARK(s(z0))) A__X(x0, s(and(x1, x2))) -> c7(A__X(mark(x0), mark(and(x1, x2)))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c18(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)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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)) 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A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) A__X(x(x0, x1), s(x2)) -> c7(A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(s(s(z0)), s(x1)) -> c7(A__PLUS(a__x(mark(s(s(z0))), mark(x1)), s(s(mark(z0)))), A__X(mark(s(s(z0))), mark(x1)), MARK(s(s(z0)))) A__X(s(and(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(and(z0, z1))), mark(x1)), s(a__and(mark(z0), z1))), A__X(mark(s(and(z0, z1))), mark(x1)), MARK(s(and(z0, z1)))) A__X(s(plus(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(plus(z0, z1))), mark(x1)), s(a__plus(mark(z0), mark(z1)))), A__X(mark(s(plus(z0, z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__X(s(x(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(x(z0, z1))), mark(x1)), s(a__x(mark(z0), mark(z1)))), A__X(mark(s(x(z0, z1))), mark(x1)), MARK(s(x(z0, z1)))) A__X(s(tt), s(x1)) -> c7(A__PLUS(a__x(mark(s(tt)), mark(x1)), s(tt)), A__X(mark(s(tt)), mark(x1)), MARK(s(tt))) A__X(s(0), s(x1)) -> c7(A__PLUS(a__x(mark(s(0)), mark(x1)), s(0)), A__X(mark(s(0)), mark(x1)), MARK(s(0))) A__X(s(x0), s(x1)) -> c7(A__PLUS(x(mark(s(x0)), mark(x1)), s(mark(x0))), A__X(mark(s(x0)), mark(x1)), MARK(s(x0))) A__X(s(x0), s(s(z0))) -> c7(A__PLUS(a__x(mark(s(x0)), s(mark(z0))), s(mark(x0))), A__X(mark(s(x0)), mark(s(z0))), MARK(s(x0))) A__X(s(x0), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__and(mark(z0), z1)), s(mark(x0))), A__X(mark(s(x0)), mark(and(z0, z1))), MARK(s(x0))) A__X(s(x0), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__plus(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(plus(z0, z1))), MARK(s(x0))) A__X(s(x0), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__x(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(x(z0, z1))), MARK(s(x0))) A__X(s(x0), s(tt)) -> c7(A__PLUS(a__x(mark(s(x0)), tt), s(mark(x0))), A__X(mark(s(x0)), mark(tt)), MARK(s(x0))) A__X(s(x0), s(0)) -> c7(A__PLUS(a__x(mark(s(x0)), 0), s(mark(x0))), A__X(mark(s(x0)), mark(0)), MARK(s(x0))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(0, s(x1)) -> c7(A__PLUS(x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(tt, s(and(x1, x2))) -> c7(A__PLUS(a__x(mark(tt), a__and(mark(x1), x2)), tt), A__X(mark(tt), mark(and(x1, x2))), MARK(tt)) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__and(mark(x1), x2)), 0), A__X(mark(0), mark(and(x1, x2))), MARK(0)) A__X(x0, s(and(x1, z1))) -> c7(A__PLUS(a__x(mark(x0), and(mark(x1), z1)), mark(x0)), A__X(mark(x0), mark(and(x1, z1))), MARK(x0)) A__X(x0, s(and(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__and(mark(z0), z1), x2)), mark(x0)), A__X(mark(x0), mark(and(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(tt, x2)), mark(x0)), A__X(mark(x0), mark(and(tt, x2))), MARK(x0)) A__X(x0, s(and(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(0, x2)), mark(x0)), A__X(mark(x0), mark(and(0, x2))), MARK(x0)) A__X(x0, s(and(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(s(mark(z0)), x2)), mark(x0)), A__X(mark(x0), mark(and(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__and(mark(x1), x2)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(and(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(and(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(and(x1, x2))), MARK(x(z0, z1))) A__X(tt, s(and(x1, x2))) -> c7(A__PLUS(a__x(tt, a__and(mark(x1), x2)), mark(tt)), A__X(mark(tt), mark(and(x1, x2))), MARK(tt)) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(0, a__and(mark(x1), x2)), mark(0)), A__X(mark(0), mark(and(x1, x2))), MARK(0)) A__X(s(z0), s(and(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__and(mark(x1), x2)), mark(s(z0))), A__X(mark(s(z0)), mark(and(x1, x2))), MARK(s(z0))) A__X(x0, s(and(x1, x2))) -> c7(A__X(mark(x0), mark(and(x1, x2)))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c4_2 ---------------------------------------- (233) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> 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s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), 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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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) A__X(x(x0, x1), s(x2)) -> c7(A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(s(s(z0)), s(x1)) -> c7(A__PLUS(a__x(mark(s(s(z0))), mark(x1)), s(s(mark(z0)))), A__X(mark(s(s(z0))), mark(x1)), MARK(s(s(z0)))) A__X(s(and(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(and(z0, z1))), mark(x1)), s(a__and(mark(z0), z1))), A__X(mark(s(and(z0, z1))), mark(x1)), MARK(s(and(z0, z1)))) A__X(s(plus(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(plus(z0, z1))), mark(x1)), s(a__plus(mark(z0), mark(z1)))), A__X(mark(s(plus(z0, z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__X(s(x(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(x(z0, z1))), mark(x1)), s(a__x(mark(z0), mark(z1)))), A__X(mark(s(x(z0, z1))), mark(x1)), MARK(s(x(z0, z1)))) A__X(s(tt), s(x1)) -> c7(A__PLUS(a__x(mark(s(tt)), mark(x1)), s(tt)), A__X(mark(s(tt)), mark(x1)), MARK(s(tt))) A__X(s(0), s(x1)) -> c7(A__PLUS(a__x(mark(s(0)), mark(x1)), s(0)), A__X(mark(s(0)), mark(x1)), MARK(s(0))) A__X(s(x0), s(x1)) -> c7(A__PLUS(x(mark(s(x0)), mark(x1)), s(mark(x0))), A__X(mark(s(x0)), mark(x1)), MARK(s(x0))) A__X(s(x0), s(s(z0))) -> c7(A__PLUS(a__x(mark(s(x0)), s(mark(z0))), s(mark(x0))), A__X(mark(s(x0)), mark(s(z0))), MARK(s(x0))) A__X(s(x0), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__and(mark(z0), z1)), s(mark(x0))), A__X(mark(s(x0)), mark(and(z0, z1))), MARK(s(x0))) A__X(s(x0), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__plus(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(plus(z0, z1))), MARK(s(x0))) A__X(s(x0), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__x(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(x(z0, z1))), MARK(s(x0))) A__X(s(x0), s(tt)) -> c7(A__PLUS(a__x(mark(s(x0)), tt), s(mark(x0))), A__X(mark(s(x0)), mark(tt)), MARK(s(x0))) A__X(s(x0), s(0)) -> c7(A__PLUS(a__x(mark(s(x0)), 0), s(mark(x0))), A__X(mark(s(x0)), mark(0)), MARK(s(x0))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(0, s(x1)) -> c7(A__PLUS(x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(x0, s(and(x1, z1))) -> c7(A__PLUS(a__x(mark(x0), and(mark(x1), z1)), mark(x0)), A__X(mark(x0), mark(and(x1, z1))), MARK(x0)) A__X(x0, s(and(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__and(mark(z0), z1), x2)), mark(x0)), A__X(mark(x0), mark(and(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(tt, x2)), mark(x0)), A__X(mark(x0), mark(and(tt, x2))), MARK(x0)) A__X(x0, s(and(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(0, x2)), mark(x0)), A__X(mark(x0), mark(and(0, x2))), MARK(x0)) A__X(x0, s(and(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(s(mark(z0)), x2)), mark(x0)), A__X(mark(x0), mark(and(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__and(mark(x1), x2)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(and(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(and(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(and(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(and(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__and(mark(x1), x2)), mark(s(z0))), A__X(mark(s(z0)), mark(and(x1, x2))), MARK(s(z0))) A__X(x0, s(and(x1, x2))) -> c7(A__X(mark(x0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__and(mark(x1), x2)), 0), A__X(mark(0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__PLUS(a__x(tt, a__and(mark(x1), x2)), mark(tt)), A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(0, a__and(mark(x1), x2)), mark(0)), A__X(mark(0), mark(and(x1, x2)))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c18(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)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> 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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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), 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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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) A__X(x(x0, x1), s(x2)) -> c7(A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(s(s(z0)), s(x1)) -> c7(A__PLUS(a__x(mark(s(s(z0))), mark(x1)), s(s(mark(z0)))), A__X(mark(s(s(z0))), mark(x1)), MARK(s(s(z0)))) A__X(s(and(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(and(z0, z1))), mark(x1)), s(a__and(mark(z0), z1))), A__X(mark(s(and(z0, z1))), mark(x1)), MARK(s(and(z0, z1)))) A__X(s(plus(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(plus(z0, z1))), mark(x1)), s(a__plus(mark(z0), mark(z1)))), A__X(mark(s(plus(z0, z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__X(s(x(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(x(z0, z1))), mark(x1)), s(a__x(mark(z0), mark(z1)))), A__X(mark(s(x(z0, z1))), mark(x1)), MARK(s(x(z0, z1)))) A__X(s(tt), s(x1)) -> c7(A__PLUS(a__x(mark(s(tt)), mark(x1)), s(tt)), A__X(mark(s(tt)), mark(x1)), MARK(s(tt))) A__X(s(0), s(x1)) -> c7(A__PLUS(a__x(mark(s(0)), mark(x1)), s(0)), A__X(mark(s(0)), mark(x1)), MARK(s(0))) A__X(s(x0), s(x1)) -> c7(A__PLUS(x(mark(s(x0)), mark(x1)), s(mark(x0))), A__X(mark(s(x0)), mark(x1)), MARK(s(x0))) A__X(s(x0), s(s(z0))) -> c7(A__PLUS(a__x(mark(s(x0)), s(mark(z0))), s(mark(x0))), A__X(mark(s(x0)), mark(s(z0))), MARK(s(x0))) A__X(s(x0), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__and(mark(z0), z1)), s(mark(x0))), A__X(mark(s(x0)), mark(and(z0, z1))), MARK(s(x0))) A__X(s(x0), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__plus(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(plus(z0, z1))), MARK(s(x0))) A__X(s(x0), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__x(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(x(z0, z1))), MARK(s(x0))) A__X(s(x0), s(tt)) -> c7(A__PLUS(a__x(mark(s(x0)), tt), s(mark(x0))), A__X(mark(s(x0)), mark(tt)), MARK(s(x0))) A__X(s(x0), s(0)) -> c7(A__PLUS(a__x(mark(s(x0)), 0), s(mark(x0))), A__X(mark(s(x0)), mark(0)), MARK(s(x0))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(0, s(x1)) -> c7(A__PLUS(x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(x0, s(and(x1, z1))) -> c7(A__PLUS(a__x(mark(x0), and(mark(x1), z1)), mark(x0)), A__X(mark(x0), mark(and(x1, z1))), MARK(x0)) A__X(x0, s(and(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__and(mark(z0), z1), x2)), mark(x0)), A__X(mark(x0), mark(and(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(tt, x2)), mark(x0)), A__X(mark(x0), mark(and(tt, x2))), MARK(x0)) A__X(x0, s(and(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(0, x2)), mark(x0)), A__X(mark(x0), mark(and(0, x2))), MARK(x0)) A__X(x0, s(and(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(s(mark(z0)), x2)), mark(x0)), A__X(mark(x0), mark(and(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__and(mark(x1), x2)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(and(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(and(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(and(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(and(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__and(mark(x1), x2)), mark(s(z0))), A__X(mark(s(z0)), mark(and(x1, x2))), MARK(s(z0))) A__X(x0, s(and(x1, x2))) -> c7(A__X(mark(x0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__and(mark(x1), x2)), 0), A__X(mark(0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__PLUS(a__x(tt, a__and(mark(x1), x2)), mark(tt)), A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(0, a__and(mark(x1), x2)), mark(0)), A__X(mark(0), mark(and(x1, x2)))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c4_2 ---------------------------------------- (235) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) by A__X(and(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(and(z0, z1)), a__plus(mark(x1), mark(x2))), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(plus(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), a__plus(mark(x1), mark(x2))), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(plus(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(x(z0, z1)), a__plus(mark(x1), mark(x2))), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(plus(x1, x2))), MARK(x(z0, z1))) A__X(tt, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(tt), a__plus(mark(x1), mark(x2))), tt), A__X(mark(tt), mark(plus(x1, x2))), MARK(tt)) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__plus(mark(x1), mark(x2))), 0), A__X(mark(0), mark(plus(x1, x2))), MARK(0)) A__X(s(z0), s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(s(z0)), a__plus(mark(x1), mark(x2))), s(mark(z0))), A__X(mark(s(z0)), mark(plus(x1, x2))), MARK(s(z0))) A__X(x0, s(plus(x1, x2))) -> c7(A__PLUS(x(mark(x0), a__plus(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x1, x2))), MARK(x0)) A__X(x0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), plus(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x1, x2))), MARK(x0)) A__X(x0, s(plus(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(plus(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(plus(x1, tt))), MARK(x0)) A__X(x0, s(plus(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(plus(x1, 0))), MARK(x0)) A__X(x0, s(plus(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(plus(x1, s(z0)))), MARK(x0)) A__X(x0, s(plus(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(tt, x2))), MARK(x0)) A__X(x0, s(plus(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(0, x2))), MARK(x0)) A__X(x0, s(plus(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(plus(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(plus(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(plus(x1, x2))), MARK(x(z0, z1))) A__X(tt, s(plus(x1, x2))) -> c7(A__PLUS(a__x(tt, a__plus(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(plus(x1, x2))), MARK(tt)) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(0, a__plus(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(plus(x1, x2))), MARK(0)) A__X(s(z0), s(plus(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__plus(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(plus(x1, x2))), MARK(s(z0))) A__X(x0, s(plus(x1, x2))) -> c7(A__X(mark(x0), mark(plus(x1, x2)))) ---------------------------------------- (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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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), 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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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), 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s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> 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x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) A__X(x(x0, x1), s(x2)) -> c7(A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(s(s(z0)), s(x1)) -> c7(A__PLUS(a__x(mark(s(s(z0))), mark(x1)), s(s(mark(z0)))), A__X(mark(s(s(z0))), mark(x1)), MARK(s(s(z0)))) A__X(s(and(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(and(z0, z1))), mark(x1)), s(a__and(mark(z0), z1))), A__X(mark(s(and(z0, z1))), mark(x1)), MARK(s(and(z0, z1)))) A__X(s(plus(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(plus(z0, z1))), mark(x1)), s(a__plus(mark(z0), mark(z1)))), A__X(mark(s(plus(z0, z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__X(s(x(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(x(z0, z1))), mark(x1)), s(a__x(mark(z0), mark(z1)))), A__X(mark(s(x(z0, z1))), mark(x1)), MARK(s(x(z0, z1)))) A__X(s(tt), s(x1)) -> c7(A__PLUS(a__x(mark(s(tt)), mark(x1)), s(tt)), A__X(mark(s(tt)), mark(x1)), MARK(s(tt))) A__X(s(0), s(x1)) -> c7(A__PLUS(a__x(mark(s(0)), mark(x1)), s(0)), A__X(mark(s(0)), mark(x1)), MARK(s(0))) A__X(s(x0), s(x1)) -> c7(A__PLUS(x(mark(s(x0)), mark(x1)), s(mark(x0))), A__X(mark(s(x0)), mark(x1)), MARK(s(x0))) A__X(s(x0), s(s(z0))) -> c7(A__PLUS(a__x(mark(s(x0)), s(mark(z0))), s(mark(x0))), A__X(mark(s(x0)), mark(s(z0))), MARK(s(x0))) A__X(s(x0), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__and(mark(z0), z1)), s(mark(x0))), A__X(mark(s(x0)), mark(and(z0, z1))), MARK(s(x0))) A__X(s(x0), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__plus(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(plus(z0, z1))), MARK(s(x0))) A__X(s(x0), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__x(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(x(z0, z1))), MARK(s(x0))) A__X(s(x0), s(tt)) -> c7(A__PLUS(a__x(mark(s(x0)), tt), s(mark(x0))), A__X(mark(s(x0)), mark(tt)), MARK(s(x0))) A__X(s(x0), s(0)) -> c7(A__PLUS(a__x(mark(s(x0)), 0), s(mark(x0))), A__X(mark(s(x0)), mark(0)), MARK(s(x0))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(0, s(x1)) -> c7(A__PLUS(x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(x0, s(and(x1, z1))) -> c7(A__PLUS(a__x(mark(x0), and(mark(x1), z1)), mark(x0)), A__X(mark(x0), mark(and(x1, z1))), MARK(x0)) A__X(x0, s(and(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__and(mark(z0), z1), x2)), mark(x0)), A__X(mark(x0), mark(and(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(tt, x2)), mark(x0)), A__X(mark(x0), mark(and(tt, x2))), MARK(x0)) A__X(x0, s(and(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(0, x2)), mark(x0)), A__X(mark(x0), mark(and(0, x2))), MARK(x0)) A__X(x0, s(and(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(s(mark(z0)), x2)), mark(x0)), A__X(mark(x0), mark(and(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__and(mark(x1), x2)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(and(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(and(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(and(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(and(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__and(mark(x1), x2)), mark(s(z0))), A__X(mark(s(z0)), mark(and(x1, x2))), MARK(s(z0))) A__X(x0, s(and(x1, x2))) -> c7(A__X(mark(x0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__and(mark(x1), x2)), 0), A__X(mark(0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__PLUS(a__x(tt, a__and(mark(x1), x2)), mark(tt)), A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(0, a__and(mark(x1), x2)), mark(0)), A__X(mark(0), mark(and(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(tt), a__plus(mark(x1), mark(x2))), tt), A__X(mark(tt), mark(plus(x1, x2))), MARK(tt)) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__plus(mark(x1), mark(x2))), 0), A__X(mark(0), mark(plus(x1, x2))), MARK(0)) A__X(x0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), plus(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x1, x2))), MARK(x0)) A__X(x0, s(plus(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(plus(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(plus(x1, tt))), MARK(x0)) A__X(x0, s(plus(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(plus(x1, 0))), MARK(x0)) A__X(x0, s(plus(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(plus(x1, s(z0)))), MARK(x0)) A__X(x0, s(plus(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(tt, x2))), MARK(x0)) A__X(x0, s(plus(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(0, x2))), MARK(x0)) A__X(x0, s(plus(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(plus(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(plus(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(plus(x1, x2))), MARK(x(z0, z1))) A__X(tt, s(plus(x1, x2))) -> c7(A__PLUS(a__x(tt, a__plus(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(plus(x1, x2))), MARK(tt)) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(0, a__plus(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(plus(x1, x2))), MARK(0)) A__X(s(z0), s(plus(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__plus(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(plus(x1, x2))), MARK(s(z0))) A__X(x0, s(plus(x1, x2))) -> c7(A__X(mark(x0), mark(plus(x1, x2)))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c18(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)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(plus(x1, x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) A__X(x(x0, x1), s(x2)) -> c7(A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(s(s(z0)), s(x1)) -> c7(A__PLUS(a__x(mark(s(s(z0))), mark(x1)), s(s(mark(z0)))), A__X(mark(s(s(z0))), mark(x1)), MARK(s(s(z0)))) A__X(s(and(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(and(z0, z1))), mark(x1)), s(a__and(mark(z0), z1))), A__X(mark(s(and(z0, z1))), mark(x1)), MARK(s(and(z0, z1)))) A__X(s(plus(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(plus(z0, z1))), mark(x1)), s(a__plus(mark(z0), mark(z1)))), A__X(mark(s(plus(z0, z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__X(s(x(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(x(z0, z1))), mark(x1)), s(a__x(mark(z0), mark(z1)))), A__X(mark(s(x(z0, z1))), mark(x1)), MARK(s(x(z0, z1)))) A__X(s(tt), s(x1)) -> c7(A__PLUS(a__x(mark(s(tt)), mark(x1)), s(tt)), A__X(mark(s(tt)), mark(x1)), MARK(s(tt))) A__X(s(0), s(x1)) -> c7(A__PLUS(a__x(mark(s(0)), mark(x1)), s(0)), A__X(mark(s(0)), mark(x1)), MARK(s(0))) A__X(s(x0), s(x1)) -> c7(A__PLUS(x(mark(s(x0)), mark(x1)), s(mark(x0))), A__X(mark(s(x0)), mark(x1)), MARK(s(x0))) A__X(s(x0), s(s(z0))) -> c7(A__PLUS(a__x(mark(s(x0)), s(mark(z0))), s(mark(x0))), A__X(mark(s(x0)), mark(s(z0))), MARK(s(x0))) A__X(s(x0), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__and(mark(z0), z1)), s(mark(x0))), A__X(mark(s(x0)), mark(and(z0, z1))), MARK(s(x0))) A__X(s(x0), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__plus(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(plus(z0, z1))), MARK(s(x0))) A__X(s(x0), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__x(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(x(z0, z1))), MARK(s(x0))) A__X(s(x0), s(tt)) -> c7(A__PLUS(a__x(mark(s(x0)), tt), s(mark(x0))), A__X(mark(s(x0)), mark(tt)), MARK(s(x0))) A__X(s(x0), s(0)) -> c7(A__PLUS(a__x(mark(s(x0)), 0), s(mark(x0))), A__X(mark(s(x0)), mark(0)), MARK(s(x0))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(0, s(x1)) -> c7(A__PLUS(x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(x0, s(and(x1, z1))) -> c7(A__PLUS(a__x(mark(x0), and(mark(x1), z1)), mark(x0)), A__X(mark(x0), mark(and(x1, z1))), MARK(x0)) A__X(x0, s(and(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__and(mark(z0), z1), x2)), mark(x0)), A__X(mark(x0), mark(and(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(tt, x2)), mark(x0)), A__X(mark(x0), mark(and(tt, x2))), MARK(x0)) A__X(x0, s(and(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(0, x2)), mark(x0)), A__X(mark(x0), mark(and(0, x2))), MARK(x0)) A__X(x0, s(and(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(s(mark(z0)), x2)), mark(x0)), A__X(mark(x0), mark(and(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__and(mark(x1), x2)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(and(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(and(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(and(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(and(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__and(mark(x1), x2)), mark(s(z0))), A__X(mark(s(z0)), mark(and(x1, x2))), MARK(s(z0))) A__X(x0, s(and(x1, x2))) -> c7(A__X(mark(x0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__and(mark(x1), x2)), 0), A__X(mark(0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__PLUS(a__x(tt, a__and(mark(x1), x2)), mark(tt)), A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(0, a__and(mark(x1), x2)), mark(0)), A__X(mark(0), mark(and(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(tt), a__plus(mark(x1), mark(x2))), tt), A__X(mark(tt), mark(plus(x1, x2))), MARK(tt)) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__plus(mark(x1), mark(x2))), 0), A__X(mark(0), mark(plus(x1, x2))), MARK(0)) A__X(x0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), plus(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x1, x2))), MARK(x0)) A__X(x0, s(plus(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(plus(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(plus(x1, tt))), MARK(x0)) A__X(x0, s(plus(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(plus(x1, 0))), MARK(x0)) A__X(x0, s(plus(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(plus(x1, s(z0)))), MARK(x0)) A__X(x0, s(plus(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(tt, x2))), MARK(x0)) A__X(x0, s(plus(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(0, x2))), MARK(x0)) A__X(x0, s(plus(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(plus(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(plus(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(plus(x1, x2))), MARK(x(z0, z1))) A__X(tt, s(plus(x1, x2))) -> c7(A__PLUS(a__x(tt, a__plus(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(plus(x1, x2))), MARK(tt)) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(0, a__plus(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(plus(x1, x2))), MARK(0)) A__X(s(z0), s(plus(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__plus(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(plus(x1, x2))), MARK(s(z0))) A__X(x0, s(plus(x1, x2))) -> c7(A__X(mark(x0), mark(plus(x1, x2)))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c4_2 ---------------------------------------- (237) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (238) 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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, 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A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) A__X(x(x0, x1), s(x2)) -> c7(A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(s(s(z0)), s(x1)) -> c7(A__PLUS(a__x(mark(s(s(z0))), mark(x1)), s(s(mark(z0)))), A__X(mark(s(s(z0))), mark(x1)), MARK(s(s(z0)))) A__X(s(and(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(and(z0, z1))), mark(x1)), s(a__and(mark(z0), z1))), A__X(mark(s(and(z0, z1))), mark(x1)), MARK(s(and(z0, z1)))) A__X(s(plus(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(plus(z0, z1))), mark(x1)), s(a__plus(mark(z0), mark(z1)))), A__X(mark(s(plus(z0, z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__X(s(x(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(x(z0, z1))), mark(x1)), s(a__x(mark(z0), mark(z1)))), A__X(mark(s(x(z0, z1))), mark(x1)), MARK(s(x(z0, z1)))) A__X(s(tt), s(x1)) -> c7(A__PLUS(a__x(mark(s(tt)), mark(x1)), s(tt)), A__X(mark(s(tt)), mark(x1)), MARK(s(tt))) A__X(s(0), s(x1)) -> c7(A__PLUS(a__x(mark(s(0)), mark(x1)), s(0)), A__X(mark(s(0)), mark(x1)), MARK(s(0))) A__X(s(x0), s(x1)) -> c7(A__PLUS(x(mark(s(x0)), mark(x1)), s(mark(x0))), A__X(mark(s(x0)), mark(x1)), MARK(s(x0))) A__X(s(x0), s(s(z0))) -> c7(A__PLUS(a__x(mark(s(x0)), s(mark(z0))), s(mark(x0))), A__X(mark(s(x0)), mark(s(z0))), MARK(s(x0))) A__X(s(x0), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__and(mark(z0), z1)), s(mark(x0))), A__X(mark(s(x0)), mark(and(z0, z1))), MARK(s(x0))) A__X(s(x0), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__plus(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(plus(z0, z1))), MARK(s(x0))) A__X(s(x0), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__x(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(x(z0, z1))), MARK(s(x0))) A__X(s(x0), s(tt)) -> c7(A__PLUS(a__x(mark(s(x0)), tt), s(mark(x0))), A__X(mark(s(x0)), mark(tt)), MARK(s(x0))) A__X(s(x0), s(0)) -> c7(A__PLUS(a__x(mark(s(x0)), 0), s(mark(x0))), A__X(mark(s(x0)), mark(0)), MARK(s(x0))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(0, s(x1)) -> c7(A__PLUS(x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(x0, s(and(x1, z1))) -> c7(A__PLUS(a__x(mark(x0), and(mark(x1), z1)), mark(x0)), A__X(mark(x0), mark(and(x1, z1))), MARK(x0)) A__X(x0, s(and(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__and(mark(z0), z1), x2)), mark(x0)), A__X(mark(x0), mark(and(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(tt, x2)), mark(x0)), A__X(mark(x0), mark(and(tt, x2))), MARK(x0)) A__X(x0, s(and(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(0, x2)), mark(x0)), A__X(mark(x0), mark(and(0, x2))), MARK(x0)) A__X(x0, s(and(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(s(mark(z0)), x2)), mark(x0)), A__X(mark(x0), mark(and(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__and(mark(x1), x2)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(and(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(and(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(and(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(and(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__and(mark(x1), x2)), mark(s(z0))), A__X(mark(s(z0)), mark(and(x1, x2))), MARK(s(z0))) A__X(x0, s(and(x1, x2))) -> c7(A__X(mark(x0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__and(mark(x1), x2)), 0), A__X(mark(0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__PLUS(a__x(tt, a__and(mark(x1), x2)), mark(tt)), A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(0, a__and(mark(x1), x2)), mark(0)), A__X(mark(0), mark(and(x1, x2)))) A__X(x0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), plus(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x1, x2))), MARK(x0)) A__X(x0, s(plus(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(plus(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(plus(x1, tt))), MARK(x0)) A__X(x0, s(plus(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(plus(x1, 0))), MARK(x0)) A__X(x0, s(plus(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(plus(x1, s(z0)))), MARK(x0)) A__X(x0, s(plus(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(tt, x2))), MARK(x0)) A__X(x0, s(plus(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(0, x2))), MARK(x0)) A__X(x0, s(plus(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(plus(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(plus(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(plus(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(plus(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__plus(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(plus(x1, x2))), MARK(s(z0))) A__X(x0, s(plus(x1, x2))) -> c7(A__X(mark(x0), mark(plus(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__plus(mark(x1), mark(x2))), 0), A__X(mark(0), mark(plus(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__PLUS(a__x(tt, a__plus(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(0, a__plus(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(plus(x1, x2)))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c18(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)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> 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MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) A__X(x(x0, x1), s(x2)) -> c7(A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(s(s(z0)), s(x1)) -> c7(A__PLUS(a__x(mark(s(s(z0))), mark(x1)), s(s(mark(z0)))), A__X(mark(s(s(z0))), mark(x1)), MARK(s(s(z0)))) A__X(s(and(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(and(z0, z1))), mark(x1)), s(a__and(mark(z0), z1))), A__X(mark(s(and(z0, z1))), mark(x1)), MARK(s(and(z0, z1)))) A__X(s(plus(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(plus(z0, z1))), mark(x1)), s(a__plus(mark(z0), mark(z1)))), A__X(mark(s(plus(z0, z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__X(s(x(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(x(z0, z1))), mark(x1)), s(a__x(mark(z0), mark(z1)))), A__X(mark(s(x(z0, z1))), mark(x1)), MARK(s(x(z0, z1)))) A__X(s(tt), s(x1)) -> c7(A__PLUS(a__x(mark(s(tt)), mark(x1)), s(tt)), A__X(mark(s(tt)), mark(x1)), MARK(s(tt))) A__X(s(0), s(x1)) -> c7(A__PLUS(a__x(mark(s(0)), mark(x1)), s(0)), A__X(mark(s(0)), mark(x1)), MARK(s(0))) A__X(s(x0), s(x1)) -> c7(A__PLUS(x(mark(s(x0)), mark(x1)), s(mark(x0))), A__X(mark(s(x0)), mark(x1)), MARK(s(x0))) A__X(s(x0), s(s(z0))) -> c7(A__PLUS(a__x(mark(s(x0)), s(mark(z0))), s(mark(x0))), A__X(mark(s(x0)), mark(s(z0))), MARK(s(x0))) A__X(s(x0), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__and(mark(z0), z1)), s(mark(x0))), A__X(mark(s(x0)), mark(and(z0, z1))), MARK(s(x0))) A__X(s(x0), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__plus(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(plus(z0, z1))), MARK(s(x0))) A__X(s(x0), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__x(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(x(z0, z1))), MARK(s(x0))) A__X(s(x0), s(tt)) -> c7(A__PLUS(a__x(mark(s(x0)), tt), s(mark(x0))), A__X(mark(s(x0)), mark(tt)), MARK(s(x0))) A__X(s(x0), s(0)) -> c7(A__PLUS(a__x(mark(s(x0)), 0), s(mark(x0))), A__X(mark(s(x0)), mark(0)), MARK(s(x0))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(0, s(x1)) -> c7(A__PLUS(x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(x0, s(and(x1, z1))) -> c7(A__PLUS(a__x(mark(x0), and(mark(x1), z1)), mark(x0)), A__X(mark(x0), mark(and(x1, z1))), MARK(x0)) A__X(x0, s(and(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__and(mark(z0), z1), x2)), mark(x0)), A__X(mark(x0), mark(and(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(tt, x2)), mark(x0)), A__X(mark(x0), mark(and(tt, x2))), MARK(x0)) A__X(x0, s(and(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(0, x2)), mark(x0)), A__X(mark(x0), mark(and(0, x2))), MARK(x0)) A__X(x0, s(and(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(s(mark(z0)), x2)), mark(x0)), A__X(mark(x0), mark(and(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__and(mark(x1), x2)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(and(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(and(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(and(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(and(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__and(mark(x1), x2)), mark(s(z0))), A__X(mark(s(z0)), mark(and(x1, x2))), MARK(s(z0))) A__X(x0, s(and(x1, x2))) -> c7(A__X(mark(x0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__and(mark(x1), x2)), 0), A__X(mark(0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__PLUS(a__x(tt, a__and(mark(x1), x2)), mark(tt)), A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(0, a__and(mark(x1), x2)), mark(0)), A__X(mark(0), mark(and(x1, x2)))) A__X(x0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), plus(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x1, x2))), MARK(x0)) A__X(x0, s(plus(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(plus(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(plus(x1, tt))), MARK(x0)) A__X(x0, s(plus(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(plus(x1, 0))), MARK(x0)) A__X(x0, s(plus(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(plus(x1, s(z0)))), MARK(x0)) A__X(x0, s(plus(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(tt, x2))), MARK(x0)) A__X(x0, s(plus(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(0, x2))), MARK(x0)) A__X(x0, s(plus(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(plus(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(plus(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(plus(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(plus(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__plus(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(plus(x1, x2))), MARK(s(z0))) A__X(x0, s(plus(x1, x2))) -> c7(A__X(mark(x0), mark(plus(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__plus(mark(x1), mark(x2))), 0), A__X(mark(0), mark(plus(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__PLUS(a__x(tt, a__plus(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(0, a__plus(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(plus(x1, x2)))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c4_2 ---------------------------------------- (239) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) by A__X(and(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(and(z0, z1)), a__x(mark(x1), mark(x2))), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), a__x(mark(x1), mark(x2))), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(x(z0, z1)), a__x(mark(x1), mark(x2))), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x(x1, x2))), MARK(x(z0, z1))) A__X(tt, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(tt), a__x(mark(x1), mark(x2))), tt), A__X(mark(tt), mark(x(x1, x2))), MARK(tt)) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__x(mark(x1), mark(x2))), 0), A__X(mark(0), mark(x(x1, x2))), MARK(0)) A__X(s(z0), s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(s(z0)), a__x(mark(x1), mark(x2))), s(mark(z0))), A__X(mark(s(z0)), mark(x(x1, x2))), MARK(s(z0))) A__X(x0, s(x(x1, x2))) -> c7(A__PLUS(x(mark(x0), a__x(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x1, x2))), MARK(x0)) A__X(x0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), x(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x1, x2))), MARK(x0)) A__X(x0, s(x(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(x(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(x(x1, tt))), MARK(x0)) A__X(x0, s(x(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(x(x1, 0))), MARK(x0)) A__X(x0, s(x(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(x(x1, s(z0)))), MARK(x0)) A__X(x0, s(x(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(tt, x2))), MARK(x0)) A__X(x0, s(x(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(0, x2))), MARK(x0)) A__X(x0, s(x(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x(x1, x2))), MARK(x(z0, z1))) A__X(tt, s(x(x1, x2))) -> c7(A__PLUS(a__x(tt, a__x(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(x(x1, x2))), MARK(tt)) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(0, a__x(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(x(x1, x2))), MARK(0)) A__X(s(z0), s(x(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__x(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(x(x1, x2))), MARK(s(z0))) A__X(x0, s(x(x1, x2))) -> c7(A__X(mark(x0), mark(x(x1, x2)))) ---------------------------------------- (240) 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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) 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a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) A__X(x(x0, x1), s(x2)) -> c7(A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(s(s(z0)), s(x1)) -> c7(A__PLUS(a__x(mark(s(s(z0))), mark(x1)), s(s(mark(z0)))), A__X(mark(s(s(z0))), mark(x1)), MARK(s(s(z0)))) A__X(s(and(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(and(z0, z1))), mark(x1)), s(a__and(mark(z0), z1))), A__X(mark(s(and(z0, z1))), mark(x1)), MARK(s(and(z0, z1)))) A__X(s(plus(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(plus(z0, z1))), mark(x1)), s(a__plus(mark(z0), mark(z1)))), A__X(mark(s(plus(z0, z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__X(s(x(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(x(z0, z1))), mark(x1)), s(a__x(mark(z0), mark(z1)))), A__X(mark(s(x(z0, z1))), mark(x1)), MARK(s(x(z0, z1)))) A__X(s(tt), s(x1)) -> c7(A__PLUS(a__x(mark(s(tt)), mark(x1)), s(tt)), A__X(mark(s(tt)), mark(x1)), MARK(s(tt))) A__X(s(0), s(x1)) -> c7(A__PLUS(a__x(mark(s(0)), mark(x1)), s(0)), A__X(mark(s(0)), mark(x1)), MARK(s(0))) A__X(s(x0), s(x1)) -> c7(A__PLUS(x(mark(s(x0)), mark(x1)), s(mark(x0))), A__X(mark(s(x0)), mark(x1)), MARK(s(x0))) A__X(s(x0), s(s(z0))) -> c7(A__PLUS(a__x(mark(s(x0)), s(mark(z0))), s(mark(x0))), A__X(mark(s(x0)), mark(s(z0))), MARK(s(x0))) A__X(s(x0), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__and(mark(z0), z1)), s(mark(x0))), A__X(mark(s(x0)), mark(and(z0, z1))), MARK(s(x0))) A__X(s(x0), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__plus(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(plus(z0, z1))), MARK(s(x0))) A__X(s(x0), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__x(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(x(z0, z1))), MARK(s(x0))) A__X(s(x0), s(tt)) -> c7(A__PLUS(a__x(mark(s(x0)), tt), s(mark(x0))), A__X(mark(s(x0)), mark(tt)), MARK(s(x0))) A__X(s(x0), s(0)) -> c7(A__PLUS(a__x(mark(s(x0)), 0), s(mark(x0))), A__X(mark(s(x0)), mark(0)), MARK(s(x0))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(0, s(x1)) -> c7(A__PLUS(x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(x0, s(and(x1, z1))) -> c7(A__PLUS(a__x(mark(x0), and(mark(x1), z1)), mark(x0)), A__X(mark(x0), mark(and(x1, z1))), MARK(x0)) A__X(x0, s(and(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__and(mark(z0), z1), x2)), mark(x0)), A__X(mark(x0), mark(and(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(tt, x2)), mark(x0)), A__X(mark(x0), mark(and(tt, x2))), MARK(x0)) A__X(x0, s(and(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(0, x2)), mark(x0)), A__X(mark(x0), mark(and(0, x2))), MARK(x0)) A__X(x0, s(and(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(s(mark(z0)), x2)), mark(x0)), A__X(mark(x0), mark(and(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__and(mark(x1), x2)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(and(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(and(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(and(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(and(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__and(mark(x1), x2)), mark(s(z0))), A__X(mark(s(z0)), mark(and(x1, x2))), MARK(s(z0))) A__X(x0, s(and(x1, x2))) -> c7(A__X(mark(x0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__and(mark(x1), x2)), 0), A__X(mark(0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__PLUS(a__x(tt, a__and(mark(x1), x2)), mark(tt)), A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(0, a__and(mark(x1), x2)), mark(0)), A__X(mark(0), mark(and(x1, x2)))) A__X(x0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), plus(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x1, x2))), MARK(x0)) A__X(x0, s(plus(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(plus(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(plus(x1, tt))), MARK(x0)) A__X(x0, s(plus(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(plus(x1, 0))), MARK(x0)) A__X(x0, s(plus(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(plus(x1, s(z0)))), MARK(x0)) A__X(x0, s(plus(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(tt, x2))), MARK(x0)) A__X(x0, s(plus(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(0, x2))), MARK(x0)) A__X(x0, s(plus(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(plus(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(plus(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(plus(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(plus(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__plus(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(plus(x1, x2))), MARK(s(z0))) A__X(x0, s(plus(x1, x2))) -> c7(A__X(mark(x0), mark(plus(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__plus(mark(x1), mark(x2))), 0), A__X(mark(0), mark(plus(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__PLUS(a__x(tt, a__plus(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(0, a__plus(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(plus(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(tt), a__x(mark(x1), mark(x2))), tt), A__X(mark(tt), mark(x(x1, x2))), MARK(tt)) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__x(mark(x1), mark(x2))), 0), A__X(mark(0), mark(x(x1, x2))), MARK(0)) A__X(x0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), x(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x1, x2))), MARK(x0)) A__X(x0, s(x(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(x(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(x(x1, tt))), MARK(x0)) A__X(x0, s(x(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(x(x1, 0))), MARK(x0)) A__X(x0, s(x(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(x(x1, s(z0)))), MARK(x0)) A__X(x0, s(x(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(tt, x2))), MARK(x0)) A__X(x0, s(x(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(0, x2))), MARK(x0)) A__X(x0, s(x(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x(x1, x2))), MARK(x(z0, z1))) A__X(tt, s(x(x1, x2))) -> c7(A__PLUS(a__x(tt, a__x(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(x(x1, x2))), MARK(tt)) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(0, a__x(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(x(x1, x2))), MARK(0)) A__X(s(z0), s(x(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__x(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(x(x1, x2))), MARK(s(z0))) A__X(x0, s(x(x1, x2))) -> c7(A__X(mark(x0), mark(x(x1, x2)))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c18(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)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), 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A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), 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c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) A__X(x(x0, x1), s(x2)) -> c7(A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(s(s(z0)), s(x1)) -> c7(A__PLUS(a__x(mark(s(s(z0))), mark(x1)), s(s(mark(z0)))), A__X(mark(s(s(z0))), mark(x1)), MARK(s(s(z0)))) A__X(s(and(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(and(z0, z1))), mark(x1)), s(a__and(mark(z0), z1))), A__X(mark(s(and(z0, z1))), mark(x1)), MARK(s(and(z0, z1)))) A__X(s(plus(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(plus(z0, z1))), mark(x1)), s(a__plus(mark(z0), mark(z1)))), A__X(mark(s(plus(z0, z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__X(s(x(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(x(z0, z1))), mark(x1)), s(a__x(mark(z0), mark(z1)))), A__X(mark(s(x(z0, z1))), mark(x1)), MARK(s(x(z0, z1)))) A__X(s(tt), s(x1)) -> c7(A__PLUS(a__x(mark(s(tt)), mark(x1)), s(tt)), A__X(mark(s(tt)), mark(x1)), MARK(s(tt))) A__X(s(0), s(x1)) -> c7(A__PLUS(a__x(mark(s(0)), mark(x1)), s(0)), A__X(mark(s(0)), mark(x1)), MARK(s(0))) A__X(s(x0), s(x1)) -> c7(A__PLUS(x(mark(s(x0)), mark(x1)), s(mark(x0))), A__X(mark(s(x0)), mark(x1)), MARK(s(x0))) A__X(s(x0), s(s(z0))) -> c7(A__PLUS(a__x(mark(s(x0)), s(mark(z0))), s(mark(x0))), A__X(mark(s(x0)), mark(s(z0))), MARK(s(x0))) A__X(s(x0), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__and(mark(z0), z1)), s(mark(x0))), A__X(mark(s(x0)), mark(and(z0, z1))), MARK(s(x0))) A__X(s(x0), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__plus(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(plus(z0, z1))), MARK(s(x0))) A__X(s(x0), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__x(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(x(z0, z1))), MARK(s(x0))) A__X(s(x0), s(tt)) -> c7(A__PLUS(a__x(mark(s(x0)), tt), s(mark(x0))), A__X(mark(s(x0)), mark(tt)), MARK(s(x0))) A__X(s(x0), s(0)) -> c7(A__PLUS(a__x(mark(s(x0)), 0), s(mark(x0))), A__X(mark(s(x0)), mark(0)), MARK(s(x0))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(0, s(x1)) -> c7(A__PLUS(x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(x0, s(and(x1, z1))) -> c7(A__PLUS(a__x(mark(x0), and(mark(x1), z1)), mark(x0)), A__X(mark(x0), mark(and(x1, z1))), MARK(x0)) A__X(x0, s(and(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__and(mark(z0), z1), x2)), mark(x0)), A__X(mark(x0), mark(and(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(tt, x2)), mark(x0)), A__X(mark(x0), mark(and(tt, x2))), MARK(x0)) A__X(x0, s(and(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(0, x2)), mark(x0)), A__X(mark(x0), mark(and(0, x2))), MARK(x0)) A__X(x0, s(and(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(s(mark(z0)), x2)), mark(x0)), A__X(mark(x0), mark(and(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__and(mark(x1), x2)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(and(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(and(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(and(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(and(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__and(mark(x1), x2)), mark(s(z0))), A__X(mark(s(z0)), mark(and(x1, x2))), MARK(s(z0))) A__X(x0, s(and(x1, x2))) -> c7(A__X(mark(x0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__and(mark(x1), x2)), 0), A__X(mark(0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__PLUS(a__x(tt, a__and(mark(x1), x2)), mark(tt)), A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(0, a__and(mark(x1), x2)), mark(0)), A__X(mark(0), mark(and(x1, x2)))) A__X(x0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), plus(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x1, x2))), MARK(x0)) A__X(x0, s(plus(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(plus(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(plus(x1, tt))), MARK(x0)) A__X(x0, s(plus(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(plus(x1, 0))), MARK(x0)) A__X(x0, s(plus(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(plus(x1, s(z0)))), MARK(x0)) A__X(x0, s(plus(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(tt, x2))), MARK(x0)) A__X(x0, s(plus(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(0, x2))), MARK(x0)) A__X(x0, s(plus(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(plus(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(plus(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(plus(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(plus(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__plus(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(plus(x1, x2))), MARK(s(z0))) A__X(x0, s(plus(x1, x2))) -> c7(A__X(mark(x0), mark(plus(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__plus(mark(x1), mark(x2))), 0), A__X(mark(0), mark(plus(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__PLUS(a__x(tt, a__plus(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(0, a__plus(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(plus(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(tt), a__x(mark(x1), mark(x2))), tt), A__X(mark(tt), mark(x(x1, x2))), MARK(tt)) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__x(mark(x1), mark(x2))), 0), A__X(mark(0), mark(x(x1, x2))), MARK(0)) A__X(x0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), x(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x1, x2))), MARK(x0)) A__X(x0, s(x(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(x(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(x(x1, tt))), MARK(x0)) A__X(x0, s(x(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(x(x1, 0))), MARK(x0)) A__X(x0, s(x(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(x(x1, s(z0)))), MARK(x0)) A__X(x0, s(x(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(tt, x2))), MARK(x0)) A__X(x0, s(x(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(0, x2))), MARK(x0)) A__X(x0, s(x(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x(x1, x2))), MARK(x(z0, z1))) A__X(tt, s(x(x1, x2))) -> c7(A__PLUS(a__x(tt, a__x(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(x(x1, x2))), MARK(tt)) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(0, a__x(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(x(x1, x2))), MARK(0)) A__X(s(z0), s(x(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__x(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(x(x1, x2))), MARK(s(z0))) A__X(x0, s(x(x1, x2))) -> c7(A__X(mark(x0), mark(x(x1, x2)))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c4_2 ---------------------------------------- (241) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (242) 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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> 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MARK(s(plus(z0, z1)))) A__PLUS(x0, s(s(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) A__X(x(x0, x1), s(x2)) -> c7(A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(s(s(z0)), s(x1)) -> c7(A__PLUS(a__x(mark(s(s(z0))), mark(x1)), s(s(mark(z0)))), A__X(mark(s(s(z0))), mark(x1)), MARK(s(s(z0)))) A__X(s(and(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(and(z0, z1))), mark(x1)), s(a__and(mark(z0), z1))), A__X(mark(s(and(z0, z1))), mark(x1)), MARK(s(and(z0, z1)))) A__X(s(plus(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(plus(z0, z1))), mark(x1)), s(a__plus(mark(z0), mark(z1)))), A__X(mark(s(plus(z0, z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__X(s(x(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(x(z0, z1))), mark(x1)), s(a__x(mark(z0), mark(z1)))), A__X(mark(s(x(z0, z1))), mark(x1)), MARK(s(x(z0, z1)))) A__X(s(tt), s(x1)) -> c7(A__PLUS(a__x(mark(s(tt)), mark(x1)), s(tt)), A__X(mark(s(tt)), mark(x1)), MARK(s(tt))) A__X(s(0), s(x1)) -> c7(A__PLUS(a__x(mark(s(0)), mark(x1)), s(0)), A__X(mark(s(0)), mark(x1)), MARK(s(0))) A__X(s(x0), s(x1)) -> c7(A__PLUS(x(mark(s(x0)), mark(x1)), s(mark(x0))), A__X(mark(s(x0)), mark(x1)), MARK(s(x0))) A__X(s(x0), s(s(z0))) -> c7(A__PLUS(a__x(mark(s(x0)), s(mark(z0))), s(mark(x0))), A__X(mark(s(x0)), mark(s(z0))), MARK(s(x0))) A__X(s(x0), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__and(mark(z0), z1)), s(mark(x0))), A__X(mark(s(x0)), mark(and(z0, z1))), MARK(s(x0))) A__X(s(x0), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__plus(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(plus(z0, z1))), MARK(s(x0))) A__X(s(x0), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__x(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(x(z0, z1))), MARK(s(x0))) A__X(s(x0), s(tt)) -> c7(A__PLUS(a__x(mark(s(x0)), tt), s(mark(x0))), A__X(mark(s(x0)), mark(tt)), MARK(s(x0))) A__X(s(x0), s(0)) -> c7(A__PLUS(a__x(mark(s(x0)), 0), s(mark(x0))), A__X(mark(s(x0)), mark(0)), MARK(s(x0))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(0, s(x1)) -> c7(A__PLUS(x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(x0, s(and(x1, z1))) -> c7(A__PLUS(a__x(mark(x0), and(mark(x1), z1)), mark(x0)), A__X(mark(x0), mark(and(x1, z1))), MARK(x0)) A__X(x0, s(and(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__and(mark(z0), z1), x2)), mark(x0)), A__X(mark(x0), mark(and(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(tt, x2)), mark(x0)), A__X(mark(x0), mark(and(tt, x2))), MARK(x0)) A__X(x0, s(and(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(0, x2)), mark(x0)), A__X(mark(x0), mark(and(0, x2))), MARK(x0)) A__X(x0, s(and(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(s(mark(z0)), x2)), mark(x0)), A__X(mark(x0), mark(and(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__and(mark(x1), x2)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(and(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(and(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(and(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(and(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__and(mark(x1), x2)), mark(s(z0))), A__X(mark(s(z0)), mark(and(x1, x2))), MARK(s(z0))) A__X(x0, s(and(x1, x2))) -> c7(A__X(mark(x0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__and(mark(x1), x2)), 0), A__X(mark(0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__PLUS(a__x(tt, a__and(mark(x1), x2)), mark(tt)), A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(0, a__and(mark(x1), x2)), mark(0)), A__X(mark(0), mark(and(x1, x2)))) A__X(x0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), plus(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x1, x2))), MARK(x0)) A__X(x0, s(plus(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(plus(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(plus(x1, tt))), MARK(x0)) A__X(x0, s(plus(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(plus(x1, 0))), MARK(x0)) A__X(x0, s(plus(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(plus(x1, s(z0)))), MARK(x0)) A__X(x0, s(plus(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(tt, x2))), MARK(x0)) A__X(x0, s(plus(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(0, x2))), MARK(x0)) A__X(x0, s(plus(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(plus(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(plus(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(plus(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(plus(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__plus(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(plus(x1, x2))), MARK(s(z0))) A__X(x0, s(plus(x1, x2))) -> c7(A__X(mark(x0), mark(plus(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__plus(mark(x1), mark(x2))), 0), A__X(mark(0), mark(plus(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__PLUS(a__x(tt, a__plus(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(0, a__plus(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(plus(x1, x2)))) A__X(x0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), x(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x1, x2))), MARK(x0)) A__X(x0, s(x(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(x(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(x(x1, tt))), MARK(x0)) A__X(x0, s(x(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(x(x1, 0))), MARK(x0)) A__X(x0, s(x(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(x(x1, s(z0)))), MARK(x0)) A__X(x0, s(x(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(tt, x2))), MARK(x0)) A__X(x0, s(x(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(0, x2))), MARK(x0)) A__X(x0, s(x(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(x(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__x(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(x(x1, x2))), MARK(s(z0))) A__X(x0, s(x(x1, x2))) -> c7(A__X(mark(x0), mark(x(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__X(mark(tt), mark(x(x1, x2)))) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__x(mark(x1), mark(x2))), 0), A__X(mark(0), mark(x(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__PLUS(a__x(tt, a__x(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(x(x1, x2)))) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(0, a__x(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(x(x1, x2)))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c18(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)) A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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)) 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c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) A__X(x(x0, x1), s(x2)) -> c7(A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(s(s(z0)), s(x1)) -> c7(A__PLUS(a__x(mark(s(s(z0))), mark(x1)), s(s(mark(z0)))), A__X(mark(s(s(z0))), mark(x1)), MARK(s(s(z0)))) A__X(s(and(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(and(z0, z1))), mark(x1)), s(a__and(mark(z0), z1))), A__X(mark(s(and(z0, z1))), mark(x1)), MARK(s(and(z0, z1)))) A__X(s(plus(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(plus(z0, z1))), mark(x1)), s(a__plus(mark(z0), mark(z1)))), A__X(mark(s(plus(z0, z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__X(s(x(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(x(z0, z1))), mark(x1)), s(a__x(mark(z0), mark(z1)))), A__X(mark(s(x(z0, z1))), mark(x1)), MARK(s(x(z0, z1)))) A__X(s(tt), s(x1)) -> c7(A__PLUS(a__x(mark(s(tt)), mark(x1)), s(tt)), A__X(mark(s(tt)), mark(x1)), MARK(s(tt))) A__X(s(0), s(x1)) -> c7(A__PLUS(a__x(mark(s(0)), mark(x1)), s(0)), A__X(mark(s(0)), mark(x1)), MARK(s(0))) A__X(s(x0), s(x1)) -> c7(A__PLUS(x(mark(s(x0)), mark(x1)), s(mark(x0))), A__X(mark(s(x0)), mark(x1)), MARK(s(x0))) A__X(s(x0), s(s(z0))) -> c7(A__PLUS(a__x(mark(s(x0)), s(mark(z0))), s(mark(x0))), A__X(mark(s(x0)), mark(s(z0))), MARK(s(x0))) A__X(s(x0), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__and(mark(z0), z1)), s(mark(x0))), A__X(mark(s(x0)), mark(and(z0, z1))), MARK(s(x0))) A__X(s(x0), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__plus(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(plus(z0, z1))), MARK(s(x0))) A__X(s(x0), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__x(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(x(z0, z1))), MARK(s(x0))) A__X(s(x0), s(tt)) -> c7(A__PLUS(a__x(mark(s(x0)), tt), s(mark(x0))), A__X(mark(s(x0)), mark(tt)), MARK(s(x0))) A__X(s(x0), s(0)) -> c7(A__PLUS(a__x(mark(s(x0)), 0), s(mark(x0))), A__X(mark(s(x0)), mark(0)), MARK(s(x0))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(0, s(x1)) -> c7(A__PLUS(x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(x0, s(and(x1, z1))) -> c7(A__PLUS(a__x(mark(x0), and(mark(x1), z1)), mark(x0)), A__X(mark(x0), mark(and(x1, z1))), MARK(x0)) A__X(x0, s(and(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__and(mark(z0), z1), x2)), mark(x0)), A__X(mark(x0), mark(and(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(tt, x2)), mark(x0)), A__X(mark(x0), mark(and(tt, x2))), MARK(x0)) A__X(x0, s(and(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(0, x2)), mark(x0)), A__X(mark(x0), mark(and(0, x2))), MARK(x0)) A__X(x0, s(and(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(s(mark(z0)), x2)), mark(x0)), A__X(mark(x0), mark(and(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__and(mark(x1), x2)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(and(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(and(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(and(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(and(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__and(mark(x1), x2)), mark(s(z0))), A__X(mark(s(z0)), mark(and(x1, x2))), MARK(s(z0))) A__X(x0, s(and(x1, x2))) -> c7(A__X(mark(x0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__and(mark(x1), x2)), 0), A__X(mark(0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__PLUS(a__x(tt, a__and(mark(x1), x2)), mark(tt)), A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(0, a__and(mark(x1), x2)), mark(0)), A__X(mark(0), mark(and(x1, x2)))) A__X(x0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), plus(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x1, x2))), MARK(x0)) A__X(x0, s(plus(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(plus(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(plus(x1, tt))), MARK(x0)) A__X(x0, s(plus(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(plus(x1, 0))), MARK(x0)) A__X(x0, s(plus(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(plus(x1, s(z0)))), MARK(x0)) A__X(x0, s(plus(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(tt, x2))), MARK(x0)) A__X(x0, s(plus(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(0, x2))), MARK(x0)) A__X(x0, s(plus(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(plus(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(plus(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(plus(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(plus(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__plus(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(plus(x1, x2))), MARK(s(z0))) A__X(x0, s(plus(x1, x2))) -> c7(A__X(mark(x0), mark(plus(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__plus(mark(x1), mark(x2))), 0), A__X(mark(0), mark(plus(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__PLUS(a__x(tt, a__plus(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(0, a__plus(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(plus(x1, x2)))) A__X(x0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), x(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x1, x2))), MARK(x0)) A__X(x0, s(x(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(x(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(x(x1, tt))), MARK(x0)) A__X(x0, s(x(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(x(x1, 0))), MARK(x0)) A__X(x0, s(x(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(x(x1, s(z0)))), MARK(x0)) A__X(x0, s(x(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(tt, x2))), MARK(x0)) A__X(x0, s(x(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(0, x2))), MARK(x0)) A__X(x0, s(x(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(x(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__x(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(x(x1, x2))), MARK(s(z0))) A__X(x0, s(x(x1, x2))) -> c7(A__X(mark(x0), mark(x(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__X(mark(tt), mark(x(x1, x2)))) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__x(mark(x1), mark(x2))), 0), A__X(mark(0), mark(x(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__PLUS(a__x(tt, a__x(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(x(x1, x2)))) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(0, a__x(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(x(x1, x2)))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c4_2 ---------------------------------------- (243) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__X(x0, s(tt)) -> c7(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) by A__X(and(z0, z1), s(tt)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), tt), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(tt)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), tt), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(tt)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(tt)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), tt), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(tt)), MARK(x(z0, z1))) A__X(tt, s(tt)) -> c7(A__PLUS(a__x(mark(tt), tt), tt), A__X(mark(tt), mark(tt)), MARK(tt)) A__X(0, s(tt)) -> c7(A__PLUS(a__x(mark(0), tt), 0), A__X(mark(0), mark(tt)), MARK(0)) A__X(s(z0), s(tt)) -> c7(A__PLUS(a__x(mark(s(z0)), tt), s(mark(z0))), A__X(mark(s(z0)), mark(tt)), MARK(s(z0))) A__X(x0, s(tt)) -> c7(A__PLUS(x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(and(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), tt), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(tt)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), tt), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(tt)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), tt), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(tt)), MARK(x(z0, z1))) A__X(tt, s(tt)) -> c7(A__PLUS(a__x(tt, tt), mark(tt)), A__X(mark(tt), mark(tt)), MARK(tt)) A__X(0, s(tt)) -> c7(A__PLUS(a__x(0, tt), mark(0)), A__X(mark(0), mark(tt)), MARK(0)) A__X(s(z0), s(tt)) -> c7(A__PLUS(a__x(s(mark(z0)), tt), mark(s(z0))), A__X(mark(s(z0)), mark(tt)), MARK(s(z0))) A__X(x0, s(tt)) -> c7(A__X(mark(x0), mark(tt))) ---------------------------------------- (244) 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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), 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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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) A__X(x(x0, x1), s(x2)) -> c7(A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(s(s(z0)), s(x1)) -> c7(A__PLUS(a__x(mark(s(s(z0))), mark(x1)), s(s(mark(z0)))), A__X(mark(s(s(z0))), mark(x1)), MARK(s(s(z0)))) A__X(s(and(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(and(z0, z1))), mark(x1)), s(a__and(mark(z0), z1))), A__X(mark(s(and(z0, z1))), mark(x1)), MARK(s(and(z0, z1)))) A__X(s(plus(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(plus(z0, z1))), mark(x1)), s(a__plus(mark(z0), mark(z1)))), A__X(mark(s(plus(z0, z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__X(s(x(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(x(z0, z1))), mark(x1)), s(a__x(mark(z0), mark(z1)))), A__X(mark(s(x(z0, z1))), mark(x1)), MARK(s(x(z0, z1)))) A__X(s(tt), s(x1)) -> c7(A__PLUS(a__x(mark(s(tt)), mark(x1)), s(tt)), A__X(mark(s(tt)), mark(x1)), MARK(s(tt))) A__X(s(0), s(x1)) -> c7(A__PLUS(a__x(mark(s(0)), mark(x1)), s(0)), A__X(mark(s(0)), mark(x1)), MARK(s(0))) A__X(s(x0), s(x1)) -> c7(A__PLUS(x(mark(s(x0)), mark(x1)), s(mark(x0))), A__X(mark(s(x0)), mark(x1)), MARK(s(x0))) A__X(s(x0), s(s(z0))) -> c7(A__PLUS(a__x(mark(s(x0)), s(mark(z0))), s(mark(x0))), A__X(mark(s(x0)), mark(s(z0))), MARK(s(x0))) A__X(s(x0), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__and(mark(z0), z1)), s(mark(x0))), A__X(mark(s(x0)), mark(and(z0, z1))), MARK(s(x0))) A__X(s(x0), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__plus(mark(z0), 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c7(A__PLUS(a__x(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(tt, x2))), MARK(x0)) A__X(x0, s(x(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(0, x2))), MARK(x0)) A__X(x0, s(x(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(x(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__x(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(x(x1, x2))), MARK(s(z0))) A__X(x0, s(x(x1, x2))) -> c7(A__X(mark(x0), mark(x(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__X(mark(tt), mark(x(x1, x2)))) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__x(mark(x1), mark(x2))), 0), A__X(mark(0), mark(x(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__PLUS(a__x(tt, a__x(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(x(x1, x2)))) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(0, a__x(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(x(x1, x2)))) A__X(tt, s(tt)) -> c7(A__PLUS(a__x(mark(tt), tt), tt), A__X(mark(tt), mark(tt)), MARK(tt)) A__X(0, s(tt)) -> c7(A__PLUS(a__x(mark(0), tt), 0), A__X(mark(0), mark(tt)), MARK(0)) A__X(and(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), tt), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(tt)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), tt), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(tt)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), tt), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(tt)), MARK(x(z0, z1))) A__X(tt, s(tt)) -> c7(A__PLUS(a__x(tt, tt), mark(tt)), A__X(mark(tt), mark(tt)), MARK(tt)) A__X(0, s(tt)) -> c7(A__PLUS(a__x(0, tt), mark(0)), A__X(mark(0), mark(tt)), MARK(0)) A__X(s(z0), s(tt)) -> c7(A__PLUS(a__x(s(mark(z0)), tt), mark(s(z0))), A__X(mark(s(z0)), mark(tt)), MARK(s(z0))) A__X(x0, s(tt)) -> c7(A__X(mark(x0), mark(tt))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c18(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)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), x2))) -> c3(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x0)) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(and(z0, z1))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(plus(z0, z1))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(z0, z1))) A__PLUS(s(z0), s(x(x1, x2))) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(s(z0))) A__PLUS(x0, s(x(x1, x2))) -> c3(MARK(x0)) A__PLUS(tt, s(x(x1, x2))) -> c3(A__PLUS(tt, a__x(mark(x1), mark(x2)))) A__PLUS(0, s(x(x1, x2))) -> c3(A__PLUS(0, a__x(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(x(z0, z1)))) -> c3(A__PLUS(mark(x0), s(a__x(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(x(z0, z1), s(s(x1))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), s(mark(x1))), MARK(x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), MARK(and(x(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, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__plus(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(plus(x0, x(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(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(plus(x(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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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(x(z0, z1)), s(x1)) -> c3(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x1)), MARK(s(x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(plus(x1, x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) A__X(x(x0, x1), s(x2)) -> c7(A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(s(s(z0)), s(x1)) -> c7(A__PLUS(a__x(mark(s(s(z0))), mark(x1)), s(s(mark(z0)))), A__X(mark(s(s(z0))), mark(x1)), MARK(s(s(z0)))) A__X(s(and(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(and(z0, z1))), mark(x1)), s(a__and(mark(z0), z1))), A__X(mark(s(and(z0, z1))), mark(x1)), MARK(s(and(z0, z1)))) A__X(s(plus(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(plus(z0, z1))), mark(x1)), s(a__plus(mark(z0), mark(z1)))), A__X(mark(s(plus(z0, z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__X(s(x(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(x(z0, z1))), mark(x1)), s(a__x(mark(z0), mark(z1)))), A__X(mark(s(x(z0, z1))), mark(x1)), MARK(s(x(z0, z1)))) A__X(s(tt), s(x1)) -> c7(A__PLUS(a__x(mark(s(tt)), mark(x1)), s(tt)), A__X(mark(s(tt)), mark(x1)), MARK(s(tt))) A__X(s(0), s(x1)) -> c7(A__PLUS(a__x(mark(s(0)), mark(x1)), s(0)), A__X(mark(s(0)), mark(x1)), MARK(s(0))) A__X(s(x0), s(x1)) -> c7(A__PLUS(x(mark(s(x0)), mark(x1)), s(mark(x0))), A__X(mark(s(x0)), mark(x1)), MARK(s(x0))) A__X(s(x0), s(s(z0))) -> c7(A__PLUS(a__x(mark(s(x0)), s(mark(z0))), s(mark(x0))), A__X(mark(s(x0)), mark(s(z0))), MARK(s(x0))) A__X(s(x0), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__and(mark(z0), z1)), s(mark(x0))), A__X(mark(s(x0)), mark(and(z0, z1))), MARK(s(x0))) A__X(s(x0), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__plus(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(plus(z0, z1))), MARK(s(x0))) A__X(s(x0), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__x(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(x(z0, z1))), MARK(s(x0))) A__X(s(x0), s(tt)) -> c7(A__PLUS(a__x(mark(s(x0)), tt), s(mark(x0))), A__X(mark(s(x0)), mark(tt)), MARK(s(x0))) A__X(s(x0), s(0)) -> c7(A__PLUS(a__x(mark(s(x0)), 0), s(mark(x0))), A__X(mark(s(x0)), mark(0)), MARK(s(x0))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(0, s(x1)) -> c7(A__PLUS(x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(x0, s(and(x1, z1))) -> c7(A__PLUS(a__x(mark(x0), and(mark(x1), z1)), mark(x0)), A__X(mark(x0), mark(and(x1, z1))), MARK(x0)) A__X(x0, s(and(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__and(mark(z0), z1), x2)), mark(x0)), A__X(mark(x0), mark(and(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(tt, x2)), mark(x0)), A__X(mark(x0), mark(and(tt, x2))), MARK(x0)) A__X(x0, s(and(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(0, x2)), mark(x0)), A__X(mark(x0), mark(and(0, x2))), MARK(x0)) A__X(x0, s(and(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(s(mark(z0)), x2)), mark(x0)), A__X(mark(x0), mark(and(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__and(mark(x1), x2)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(and(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(and(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(and(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(and(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__and(mark(x1), x2)), mark(s(z0))), A__X(mark(s(z0)), mark(and(x1, x2))), MARK(s(z0))) A__X(x0, s(and(x1, x2))) -> c7(A__X(mark(x0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__and(mark(x1), x2)), 0), A__X(mark(0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__PLUS(a__x(tt, a__and(mark(x1), x2)), mark(tt)), A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(0, a__and(mark(x1), x2)), mark(0)), A__X(mark(0), mark(and(x1, x2)))) A__X(x0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), plus(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x1, x2))), MARK(x0)) A__X(x0, s(plus(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(plus(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(plus(x1, tt))), MARK(x0)) A__X(x0, s(plus(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(plus(x1, 0))), MARK(x0)) A__X(x0, s(plus(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(plus(x1, s(z0)))), MARK(x0)) A__X(x0, s(plus(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(tt, x2))), MARK(x0)) A__X(x0, s(plus(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(0, x2))), MARK(x0)) A__X(x0, s(plus(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(plus(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(plus(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(plus(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(plus(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__plus(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(plus(x1, x2))), MARK(s(z0))) A__X(x0, s(plus(x1, x2))) -> c7(A__X(mark(x0), mark(plus(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__plus(mark(x1), mark(x2))), 0), A__X(mark(0), mark(plus(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__PLUS(a__x(tt, a__plus(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(0, a__plus(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(plus(x1, x2)))) A__X(x0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), x(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x1, x2))), MARK(x0)) A__X(x0, s(x(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(x(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(x(x1, tt))), MARK(x0)) A__X(x0, s(x(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(x(x1, 0))), MARK(x0)) A__X(x0, s(x(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(x(x1, s(z0)))), MARK(x0)) A__X(x0, s(x(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(tt, x2))), MARK(x0)) A__X(x0, s(x(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(0, x2))), MARK(x0)) A__X(x0, s(x(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(x(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__x(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(x(x1, x2))), MARK(s(z0))) A__X(x0, s(x(x1, x2))) -> c7(A__X(mark(x0), mark(x(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__X(mark(tt), mark(x(x1, x2)))) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__x(mark(x1), mark(x2))), 0), A__X(mark(0), mark(x(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__PLUS(a__x(tt, a__x(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(x(x1, x2)))) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(0, a__x(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(x(x1, x2)))) A__X(tt, s(tt)) -> c7(A__PLUS(a__x(mark(tt), tt), tt), A__X(mark(tt), mark(tt)), MARK(tt)) A__X(0, s(tt)) -> c7(A__PLUS(a__x(mark(0), tt), 0), A__X(mark(0), mark(tt)), MARK(0)) A__X(and(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), tt), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(tt)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), tt), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(tt)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), tt), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(tt)), MARK(x(z0, z1))) A__X(tt, s(tt)) -> c7(A__PLUS(a__x(tt, tt), mark(tt)), A__X(mark(tt), mark(tt)), MARK(tt)) A__X(0, s(tt)) -> c7(A__PLUS(a__x(0, tt), mark(0)), A__X(mark(0), mark(tt)), MARK(0)) A__X(s(z0), s(tt)) -> c7(A__PLUS(a__x(s(mark(z0)), tt), mark(s(z0))), A__X(mark(s(z0)), mark(tt)), MARK(s(z0))) A__X(x0, s(tt)) -> c7(A__X(mark(x0), mark(tt))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c4_2 ---------------------------------------- (245) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (246) 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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> 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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(x(x0, x1), s(0)) -> c3(A__PLUS(a__x(mark(x0), mark(x1)), 0), MARK(x(x0, x1))) A__PLUS(x(x0, x1), s(x2)) -> c3(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x(x0, x1))) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x(x0, and(z0, z1)))) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__PLUS(x(x0, tt), s(x2)) -> c3(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x(x0, tt))) A__PLUS(x(x0, 0), s(x2)) -> c3(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x(x0, 0))) A__PLUS(x(x0, s(z0)), s(x2)) -> c3(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__PLUS(x(tt, x1), s(x2)) -> c3(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x(tt, x1))) A__PLUS(x(0, x1), s(x2)) -> c3(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x(0, x1))) A__PLUS(x(s(z0), x1), s(x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x(s(z0), x1))) A__PLUS(x(x0, x1), s(tt)) -> c3(MARK(x(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)))) 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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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) A__X(x(x0, x1), s(x2)) -> c7(A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(s(s(z0)), s(x1)) -> c7(A__PLUS(a__x(mark(s(s(z0))), mark(x1)), s(s(mark(z0)))), A__X(mark(s(s(z0))), mark(x1)), MARK(s(s(z0)))) A__X(s(and(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(and(z0, z1))), mark(x1)), s(a__and(mark(z0), z1))), A__X(mark(s(and(z0, z1))), mark(x1)), MARK(s(and(z0, z1)))) A__X(s(plus(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(plus(z0, z1))), mark(x1)), s(a__plus(mark(z0), mark(z1)))), A__X(mark(s(plus(z0, z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__X(s(x(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(x(z0, z1))), mark(x1)), s(a__x(mark(z0), mark(z1)))), A__X(mark(s(x(z0, z1))), mark(x1)), MARK(s(x(z0, z1)))) A__X(s(tt), s(x1)) -> c7(A__PLUS(a__x(mark(s(tt)), mark(x1)), s(tt)), A__X(mark(s(tt)), mark(x1)), MARK(s(tt))) A__X(s(0), s(x1)) -> c7(A__PLUS(a__x(mark(s(0)), mark(x1)), s(0)), A__X(mark(s(0)), mark(x1)), MARK(s(0))) A__X(s(x0), s(x1)) -> c7(A__PLUS(x(mark(s(x0)), mark(x1)), s(mark(x0))), A__X(mark(s(x0)), mark(x1)), MARK(s(x0))) A__X(s(x0), s(s(z0))) -> c7(A__PLUS(a__x(mark(s(x0)), s(mark(z0))), s(mark(x0))), A__X(mark(s(x0)), mark(s(z0))), MARK(s(x0))) A__X(s(x0), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__and(mark(z0), z1)), s(mark(x0))), A__X(mark(s(x0)), mark(and(z0, z1))), MARK(s(x0))) A__X(s(x0), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__plus(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(plus(z0, z1))), MARK(s(x0))) A__X(s(x0), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__x(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(x(z0, z1))), MARK(s(x0))) A__X(s(x0), s(tt)) -> c7(A__PLUS(a__x(mark(s(x0)), tt), s(mark(x0))), A__X(mark(s(x0)), mark(tt)), MARK(s(x0))) A__X(s(x0), s(0)) -> c7(A__PLUS(a__x(mark(s(x0)), 0), s(mark(x0))), A__X(mark(s(x0)), mark(0)), MARK(s(x0))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(0, s(x1)) -> c7(A__PLUS(x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(x0, s(and(x1, z1))) -> c7(A__PLUS(a__x(mark(x0), and(mark(x1), z1)), mark(x0)), A__X(mark(x0), mark(and(x1, z1))), MARK(x0)) A__X(x0, s(and(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__and(mark(z0), z1), x2)), mark(x0)), A__X(mark(x0), mark(and(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(tt, x2)), mark(x0)), A__X(mark(x0), mark(and(tt, x2))), MARK(x0)) A__X(x0, s(and(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(0, x2)), mark(x0)), A__X(mark(x0), mark(and(0, x2))), MARK(x0)) A__X(x0, s(and(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(s(mark(z0)), x2)), mark(x0)), A__X(mark(x0), mark(and(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__and(mark(x1), x2)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(and(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(and(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(and(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(and(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__and(mark(x1), x2)), mark(s(z0))), A__X(mark(s(z0)), mark(and(x1, x2))), MARK(s(z0))) A__X(x0, s(and(x1, x2))) -> c7(A__X(mark(x0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__and(mark(x1), x2)), 0), A__X(mark(0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__PLUS(a__x(tt, a__and(mark(x1), x2)), mark(tt)), A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(0, a__and(mark(x1), x2)), mark(0)), A__X(mark(0), mark(and(x1, x2)))) A__X(x0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), plus(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x1, x2))), MARK(x0)) A__X(x0, s(plus(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(plus(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(plus(x1, tt))), MARK(x0)) A__X(x0, s(plus(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(plus(x1, 0))), MARK(x0)) A__X(x0, s(plus(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(plus(x1, s(z0)))), MARK(x0)) A__X(x0, s(plus(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(tt, x2))), MARK(x0)) A__X(x0, s(plus(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(0, x2))), MARK(x0)) A__X(x0, s(plus(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(plus(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(plus(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(plus(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(plus(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__plus(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(plus(x1, x2))), MARK(s(z0))) A__X(x0, s(plus(x1, x2))) -> c7(A__X(mark(x0), mark(plus(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__plus(mark(x1), mark(x2))), 0), A__X(mark(0), mark(plus(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__PLUS(a__x(tt, a__plus(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(0, a__plus(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(plus(x1, x2)))) A__X(x0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), x(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x1, x2))), MARK(x0)) A__X(x0, s(x(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(x(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(x(x1, tt))), MARK(x0)) A__X(x0, s(x(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(x(x1, 0))), MARK(x0)) A__X(x0, s(x(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(x(x1, s(z0)))), MARK(x0)) A__X(x0, s(x(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(tt, x2))), MARK(x0)) A__X(x0, s(x(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(0, x2))), MARK(x0)) A__X(x0, s(x(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(x(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__x(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(x(x1, x2))), MARK(s(z0))) A__X(x0, s(x(x1, x2))) -> c7(A__X(mark(x0), mark(x(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__X(mark(tt), mark(x(x1, x2)))) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__x(mark(x1), mark(x2))), 0), A__X(mark(0), mark(x(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__PLUS(a__x(tt, a__x(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(x(x1, x2)))) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(0, a__x(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(x(x1, x2)))) A__X(and(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), tt), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(tt)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), tt), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(tt)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), tt), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(tt)), MARK(x(z0, z1))) A__X(s(z0), s(tt)) -> c7(A__PLUS(a__x(s(mark(z0)), tt), mark(s(z0))), A__X(mark(s(z0)), mark(tt)), MARK(s(z0))) A__X(x0, s(tt)) -> c7(A__X(mark(x0), mark(tt))) A__X(tt, s(tt)) -> c7(A__X(mark(tt), mark(tt))) A__X(0, s(tt)) -> c7(A__PLUS(a__x(mark(0), tt), 0), A__X(mark(0), mark(tt))) A__X(tt, s(tt)) -> c7(A__PLUS(a__x(tt, tt), mark(tt)), A__X(mark(tt), mark(tt))) A__X(0, s(tt)) -> c7(A__PLUS(a__x(0, tt), mark(0)), A__X(mark(0), mark(tt))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c18(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)) A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), 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c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 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MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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), 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s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> 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x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), 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c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) A__X(x(x0, x1), s(x2)) -> c7(A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(s(s(z0)), s(x1)) -> c7(A__PLUS(a__x(mark(s(s(z0))), mark(x1)), s(s(mark(z0)))), A__X(mark(s(s(z0))), mark(x1)), MARK(s(s(z0)))) A__X(s(and(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(and(z0, z1))), mark(x1)), s(a__and(mark(z0), z1))), A__X(mark(s(and(z0, z1))), mark(x1)), MARK(s(and(z0, z1)))) A__X(s(plus(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(plus(z0, z1))), mark(x1)), s(a__plus(mark(z0), mark(z1)))), A__X(mark(s(plus(z0, z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__X(s(x(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(x(z0, z1))), mark(x1)), s(a__x(mark(z0), mark(z1)))), A__X(mark(s(x(z0, z1))), mark(x1)), MARK(s(x(z0, z1)))) A__X(s(tt), s(x1)) -> c7(A__PLUS(a__x(mark(s(tt)), mark(x1)), s(tt)), A__X(mark(s(tt)), mark(x1)), MARK(s(tt))) A__X(s(0), s(x1)) -> c7(A__PLUS(a__x(mark(s(0)), mark(x1)), s(0)), A__X(mark(s(0)), mark(x1)), MARK(s(0))) A__X(s(x0), s(x1)) -> c7(A__PLUS(x(mark(s(x0)), mark(x1)), s(mark(x0))), A__X(mark(s(x0)), mark(x1)), MARK(s(x0))) A__X(s(x0), s(s(z0))) -> c7(A__PLUS(a__x(mark(s(x0)), s(mark(z0))), s(mark(x0))), A__X(mark(s(x0)), mark(s(z0))), MARK(s(x0))) A__X(s(x0), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__and(mark(z0), z1)), s(mark(x0))), A__X(mark(s(x0)), mark(and(z0, z1))), MARK(s(x0))) A__X(s(x0), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__plus(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(plus(z0, z1))), MARK(s(x0))) A__X(s(x0), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__x(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(x(z0, z1))), MARK(s(x0))) A__X(s(x0), s(tt)) -> c7(A__PLUS(a__x(mark(s(x0)), tt), s(mark(x0))), A__X(mark(s(x0)), mark(tt)), MARK(s(x0))) A__X(s(x0), s(0)) -> c7(A__PLUS(a__x(mark(s(x0)), 0), s(mark(x0))), A__X(mark(s(x0)), mark(0)), MARK(s(x0))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(0, s(x1)) -> c7(A__PLUS(x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(x0, s(and(x1, z1))) -> c7(A__PLUS(a__x(mark(x0), and(mark(x1), z1)), mark(x0)), A__X(mark(x0), mark(and(x1, z1))), MARK(x0)) A__X(x0, s(and(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__and(mark(z0), z1), x2)), mark(x0)), A__X(mark(x0), mark(and(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(tt, x2)), mark(x0)), A__X(mark(x0), mark(and(tt, x2))), MARK(x0)) A__X(x0, s(and(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(0, x2)), mark(x0)), A__X(mark(x0), mark(and(0, x2))), MARK(x0)) A__X(x0, s(and(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(s(mark(z0)), x2)), mark(x0)), A__X(mark(x0), mark(and(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__and(mark(x1), x2)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(and(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(and(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(and(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(and(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__and(mark(x1), x2)), mark(s(z0))), A__X(mark(s(z0)), mark(and(x1, x2))), MARK(s(z0))) A__X(x0, s(and(x1, x2))) -> c7(A__X(mark(x0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__and(mark(x1), x2)), 0), A__X(mark(0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__PLUS(a__x(tt, a__and(mark(x1), x2)), mark(tt)), A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(0, a__and(mark(x1), x2)), mark(0)), A__X(mark(0), mark(and(x1, x2)))) A__X(x0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), plus(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x1, x2))), MARK(x0)) A__X(x0, s(plus(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(plus(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(plus(x1, tt))), MARK(x0)) A__X(x0, s(plus(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(plus(x1, 0))), MARK(x0)) A__X(x0, s(plus(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(plus(x1, s(z0)))), MARK(x0)) A__X(x0, s(plus(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(tt, x2))), MARK(x0)) A__X(x0, s(plus(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(0, x2))), MARK(x0)) A__X(x0, s(plus(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(plus(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(plus(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(plus(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(plus(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__plus(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(plus(x1, x2))), MARK(s(z0))) A__X(x0, s(plus(x1, x2))) -> c7(A__X(mark(x0), mark(plus(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__plus(mark(x1), mark(x2))), 0), A__X(mark(0), mark(plus(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__PLUS(a__x(tt, a__plus(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(0, a__plus(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(plus(x1, x2)))) A__X(x0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), x(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x1, x2))), MARK(x0)) A__X(x0, s(x(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(x(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(x(x1, tt))), MARK(x0)) A__X(x0, s(x(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(x(x1, 0))), MARK(x0)) A__X(x0, s(x(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(x(x1, s(z0)))), MARK(x0)) A__X(x0, s(x(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(tt, x2))), MARK(x0)) A__X(x0, s(x(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(0, x2))), MARK(x0)) A__X(x0, s(x(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(x(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__x(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(x(x1, x2))), MARK(s(z0))) A__X(x0, s(x(x1, x2))) -> c7(A__X(mark(x0), mark(x(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__X(mark(tt), mark(x(x1, x2)))) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__x(mark(x1), mark(x2))), 0), A__X(mark(0), mark(x(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__PLUS(a__x(tt, a__x(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(x(x1, x2)))) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(0, a__x(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(x(x1, x2)))) A__X(and(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), tt), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(tt)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), tt), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(tt)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), tt), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(tt)), MARK(x(z0, z1))) A__X(s(z0), s(tt)) -> c7(A__PLUS(a__x(s(mark(z0)), tt), mark(s(z0))), A__X(mark(s(z0)), mark(tt)), MARK(s(z0))) A__X(x0, s(tt)) -> c7(A__X(mark(x0), mark(tt))) A__X(tt, s(tt)) -> c7(A__X(mark(tt), mark(tt))) A__X(0, s(tt)) -> c7(A__PLUS(a__x(mark(0), tt), 0), A__X(mark(0), mark(tt))) A__X(tt, s(tt)) -> c7(A__PLUS(a__x(tt, tt), mark(tt)), A__X(mark(tt), mark(tt))) A__X(0, s(tt)) -> c7(A__PLUS(a__x(0, tt), mark(0)), A__X(mark(0), mark(tt))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c4_2 ---------------------------------------- (247) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__X(x0, s(0)) -> c7(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) by A__X(and(z0, z1), s(0)) -> c7(A__PLUS(a__x(mark(and(z0, z1)), 0), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(0)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(0)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), 0), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(0)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(0)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), 0), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(0)), MARK(x(z0, z1))) A__X(tt, s(0)) -> c7(A__PLUS(a__x(mark(tt), 0), tt), A__X(mark(tt), mark(0)), MARK(tt)) A__X(0, s(0)) -> c7(A__PLUS(a__x(mark(0), 0), 0), A__X(mark(0), mark(0)), MARK(0)) A__X(s(z0), s(0)) -> c7(A__PLUS(a__x(mark(s(z0)), 0), s(mark(z0))), A__X(mark(s(z0)), mark(0)), MARK(s(z0))) A__X(x0, s(0)) -> c7(A__PLUS(0, mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(and(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), 0), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(0)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), 0), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(0)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), 0), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(0)), MARK(x(z0, z1))) A__X(tt, s(0)) -> c7(A__PLUS(a__x(tt, 0), mark(tt)), A__X(mark(tt), mark(0)), MARK(tt)) A__X(0, s(0)) -> c7(A__PLUS(a__x(0, 0), mark(0)), A__X(mark(0), mark(0)), MARK(0)) A__X(s(z0), s(0)) -> c7(A__PLUS(a__x(s(mark(z0)), 0), mark(s(z0))), A__X(mark(s(z0)), mark(0)), MARK(s(z0))) A__X(x0, s(0)) -> c7(A__X(mark(x0), mark(0))) ---------------------------------------- (248) 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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> 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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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) A__X(x(x0, x1), s(x2)) -> c7(A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(s(s(z0)), s(x1)) -> c7(A__PLUS(a__x(mark(s(s(z0))), mark(x1)), s(s(mark(z0)))), A__X(mark(s(s(z0))), mark(x1)), MARK(s(s(z0)))) A__X(s(and(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(and(z0, z1))), mark(x1)), s(a__and(mark(z0), z1))), A__X(mark(s(and(z0, z1))), mark(x1)), MARK(s(and(z0, z1)))) A__X(s(plus(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(plus(z0, z1))), mark(x1)), s(a__plus(mark(z0), mark(z1)))), A__X(mark(s(plus(z0, z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__X(s(x(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(x(z0, z1))), mark(x1)), s(a__x(mark(z0), mark(z1)))), A__X(mark(s(x(z0, z1))), mark(x1)), MARK(s(x(z0, z1)))) A__X(s(tt), s(x1)) -> c7(A__PLUS(a__x(mark(s(tt)), mark(x1)), s(tt)), A__X(mark(s(tt)), mark(x1)), MARK(s(tt))) A__X(s(0), s(x1)) -> c7(A__PLUS(a__x(mark(s(0)), mark(x1)), s(0)), A__X(mark(s(0)), mark(x1)), MARK(s(0))) A__X(s(x0), s(x1)) -> c7(A__PLUS(x(mark(s(x0)), mark(x1)), s(mark(x0))), A__X(mark(s(x0)), mark(x1)), MARK(s(x0))) A__X(s(x0), s(s(z0))) -> c7(A__PLUS(a__x(mark(s(x0)), s(mark(z0))), s(mark(x0))), A__X(mark(s(x0)), mark(s(z0))), MARK(s(x0))) A__X(s(x0), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__and(mark(z0), z1)), s(mark(x0))), A__X(mark(s(x0)), mark(and(z0, z1))), MARK(s(x0))) A__X(s(x0), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__plus(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(plus(z0, z1))), MARK(s(x0))) A__X(s(x0), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__x(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(x(z0, z1))), MARK(s(x0))) A__X(s(x0), s(tt)) -> c7(A__PLUS(a__x(mark(s(x0)), tt), s(mark(x0))), A__X(mark(s(x0)), mark(tt)), MARK(s(x0))) A__X(s(x0), s(0)) -> c7(A__PLUS(a__x(mark(s(x0)), 0), s(mark(x0))), A__X(mark(s(x0)), mark(0)), MARK(s(x0))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(0, s(x1)) -> c7(A__PLUS(x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(x0, s(and(x1, z1))) -> c7(A__PLUS(a__x(mark(x0), and(mark(x1), z1)), mark(x0)), A__X(mark(x0), mark(and(x1, z1))), MARK(x0)) A__X(x0, s(and(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__and(mark(z0), z1), x2)), mark(x0)), A__X(mark(x0), mark(and(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(plus(z0, 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mark(plus(x1, x2))), MARK(x0)) A__X(x0, s(plus(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(plus(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(plus(x1, tt))), MARK(x0)) A__X(x0, s(plus(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(plus(x1, 0))), MARK(x0)) A__X(x0, s(plus(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(plus(x1, s(z0)))), MARK(x0)) A__X(x0, s(plus(and(z0, 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mark(tt)), A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(0, a__plus(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(plus(x1, x2)))) A__X(x0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), x(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x1, x2))), MARK(x0)) A__X(x0, s(x(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(x(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(x(x1, tt))), MARK(x0)) A__X(x0, s(x(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), 0)), 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a__x(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(x(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__x(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(x(x1, x2))), MARK(s(z0))) A__X(x0, s(x(x1, x2))) -> c7(A__X(mark(x0), mark(x(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__X(mark(tt), mark(x(x1, x2)))) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__x(mark(x1), mark(x2))), 0), A__X(mark(0), mark(x(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__PLUS(a__x(tt, a__x(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(x(x1, x2)))) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(0, a__x(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(x(x1, x2)))) A__X(and(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), tt), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(tt)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), tt), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(tt)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), tt), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(tt)), MARK(x(z0, z1))) A__X(s(z0), s(tt)) -> c7(A__PLUS(a__x(s(mark(z0)), tt), mark(s(z0))), A__X(mark(s(z0)), mark(tt)), MARK(s(z0))) A__X(x0, s(tt)) -> c7(A__X(mark(x0), mark(tt))) A__X(tt, s(tt)) -> c7(A__X(mark(tt), mark(tt))) A__X(0, s(tt)) -> c7(A__PLUS(a__x(mark(0), tt), 0), A__X(mark(0), mark(tt))) A__X(tt, s(tt)) -> c7(A__PLUS(a__x(tt, tt), mark(tt)), A__X(mark(tt), mark(tt))) A__X(0, s(tt)) -> c7(A__PLUS(a__x(0, tt), mark(0)), A__X(mark(0), mark(tt))) A__X(tt, s(0)) -> c7(A__PLUS(a__x(mark(tt), 0), tt), A__X(mark(tt), mark(0)), MARK(tt)) A__X(0, s(0)) -> c7(A__PLUS(a__x(mark(0), 0), 0), A__X(mark(0), mark(0)), MARK(0)) A__X(x0, s(0)) -> c7(A__PLUS(0, mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(and(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), 0), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(0)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), 0), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(0)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), 0), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(0)), MARK(x(z0, z1))) A__X(tt, s(0)) -> c7(A__PLUS(a__x(tt, 0), mark(tt)), A__X(mark(tt), mark(0)), MARK(tt)) A__X(0, s(0)) -> c7(A__PLUS(a__x(0, 0), mark(0)), A__X(mark(0), mark(0)), MARK(0)) A__X(s(z0), s(0)) -> c7(A__PLUS(a__x(s(mark(z0)), 0), mark(s(z0))), A__X(mark(s(z0)), mark(0)), MARK(s(z0))) A__X(x0, s(0)) -> c7(A__X(mark(x0), mark(0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c18(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)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), 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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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, 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plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) A__X(x(x0, x1), s(x2)) -> c7(A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(s(s(z0)), s(x1)) -> c7(A__PLUS(a__x(mark(s(s(z0))), mark(x1)), s(s(mark(z0)))), A__X(mark(s(s(z0))), mark(x1)), MARK(s(s(z0)))) A__X(s(and(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(and(z0, z1))), mark(x1)), s(a__and(mark(z0), z1))), A__X(mark(s(and(z0, z1))), mark(x1)), MARK(s(and(z0, z1)))) A__X(s(plus(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(plus(z0, z1))), mark(x1)), s(a__plus(mark(z0), mark(z1)))), A__X(mark(s(plus(z0, z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__X(s(x(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(x(z0, z1))), mark(x1)), s(a__x(mark(z0), mark(z1)))), A__X(mark(s(x(z0, z1))), mark(x1)), MARK(s(x(z0, z1)))) A__X(s(tt), s(x1)) -> c7(A__PLUS(a__x(mark(s(tt)), mark(x1)), s(tt)), A__X(mark(s(tt)), mark(x1)), MARK(s(tt))) A__X(s(0), s(x1)) -> c7(A__PLUS(a__x(mark(s(0)), mark(x1)), s(0)), A__X(mark(s(0)), mark(x1)), MARK(s(0))) A__X(s(x0), s(x1)) -> c7(A__PLUS(x(mark(s(x0)), mark(x1)), s(mark(x0))), A__X(mark(s(x0)), mark(x1)), MARK(s(x0))) A__X(s(x0), s(s(z0))) -> c7(A__PLUS(a__x(mark(s(x0)), s(mark(z0))), s(mark(x0))), A__X(mark(s(x0)), mark(s(z0))), MARK(s(x0))) A__X(s(x0), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__and(mark(z0), z1)), s(mark(x0))), A__X(mark(s(x0)), mark(and(z0, z1))), MARK(s(x0))) A__X(s(x0), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__plus(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(plus(z0, z1))), MARK(s(x0))) A__X(s(x0), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__x(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(x(z0, z1))), MARK(s(x0))) A__X(s(x0), s(tt)) -> c7(A__PLUS(a__x(mark(s(x0)), tt), s(mark(x0))), A__X(mark(s(x0)), mark(tt)), MARK(s(x0))) A__X(s(x0), s(0)) -> c7(A__PLUS(a__x(mark(s(x0)), 0), s(mark(x0))), A__X(mark(s(x0)), mark(0)), MARK(s(x0))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(0, s(x1)) -> c7(A__PLUS(x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(x0, s(and(x1, z1))) -> c7(A__PLUS(a__x(mark(x0), and(mark(x1), z1)), mark(x0)), A__X(mark(x0), mark(and(x1, z1))), MARK(x0)) A__X(x0, s(and(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__and(mark(z0), z1), x2)), mark(x0)), A__X(mark(x0), mark(and(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(tt, x2)), mark(x0)), A__X(mark(x0), mark(and(tt, x2))), MARK(x0)) A__X(x0, s(and(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(0, x2)), mark(x0)), A__X(mark(x0), mark(and(0, x2))), MARK(x0)) A__X(x0, s(and(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(s(mark(z0)), x2)), mark(x0)), A__X(mark(x0), mark(and(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__and(mark(x1), x2)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(and(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(and(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(and(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(and(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__and(mark(x1), x2)), mark(s(z0))), A__X(mark(s(z0)), mark(and(x1, x2))), MARK(s(z0))) A__X(x0, s(and(x1, x2))) -> c7(A__X(mark(x0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__and(mark(x1), x2)), 0), A__X(mark(0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__PLUS(a__x(tt, a__and(mark(x1), x2)), mark(tt)), A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(0, a__and(mark(x1), x2)), mark(0)), A__X(mark(0), mark(and(x1, x2)))) A__X(x0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), plus(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x1, x2))), MARK(x0)) A__X(x0, s(plus(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(plus(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(plus(x1, tt))), MARK(x0)) A__X(x0, s(plus(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(plus(x1, 0))), MARK(x0)) A__X(x0, s(plus(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(plus(x1, s(z0)))), MARK(x0)) A__X(x0, s(plus(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(tt, x2))), MARK(x0)) A__X(x0, s(plus(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(0, x2))), MARK(x0)) A__X(x0, s(plus(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(plus(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(plus(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(plus(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(plus(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__plus(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(plus(x1, x2))), MARK(s(z0))) A__X(x0, s(plus(x1, x2))) -> c7(A__X(mark(x0), mark(plus(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__plus(mark(x1), mark(x2))), 0), A__X(mark(0), mark(plus(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__PLUS(a__x(tt, a__plus(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(0, a__plus(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(plus(x1, x2)))) A__X(x0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), x(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x1, x2))), MARK(x0)) A__X(x0, s(x(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(x(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(x(x1, tt))), MARK(x0)) A__X(x0, s(x(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(x(x1, 0))), MARK(x0)) A__X(x0, s(x(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(x(x1, s(z0)))), MARK(x0)) A__X(x0, s(x(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(tt, x2))), MARK(x0)) A__X(x0, s(x(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(0, x2))), MARK(x0)) A__X(x0, s(x(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(x(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__x(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(x(x1, x2))), MARK(s(z0))) A__X(x0, s(x(x1, x2))) -> c7(A__X(mark(x0), mark(x(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__X(mark(tt), mark(x(x1, x2)))) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__x(mark(x1), mark(x2))), 0), A__X(mark(0), mark(x(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__PLUS(a__x(tt, a__x(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(x(x1, x2)))) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(0, a__x(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(x(x1, x2)))) A__X(and(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), tt), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(tt)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), tt), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(tt)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), tt), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(tt)), MARK(x(z0, z1))) A__X(s(z0), s(tt)) -> c7(A__PLUS(a__x(s(mark(z0)), tt), mark(s(z0))), A__X(mark(s(z0)), mark(tt)), MARK(s(z0))) A__X(x0, s(tt)) -> c7(A__X(mark(x0), mark(tt))) A__X(tt, s(tt)) -> c7(A__X(mark(tt), mark(tt))) A__X(0, s(tt)) -> c7(A__PLUS(a__x(mark(0), tt), 0), A__X(mark(0), mark(tt))) A__X(tt, s(tt)) -> c7(A__PLUS(a__x(tt, tt), mark(tt)), A__X(mark(tt), mark(tt))) A__X(0, s(tt)) -> c7(A__PLUS(a__x(0, tt), mark(0)), A__X(mark(0), mark(tt))) A__X(tt, s(0)) -> c7(A__PLUS(a__x(mark(tt), 0), tt), A__X(mark(tt), mark(0)), MARK(tt)) A__X(0, s(0)) -> c7(A__PLUS(a__x(mark(0), 0), 0), A__X(mark(0), mark(0)), MARK(0)) A__X(x0, s(0)) -> c7(A__PLUS(0, mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(and(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), 0), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(0)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), 0), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(0)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), 0), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(0)), MARK(x(z0, z1))) A__X(tt, s(0)) -> c7(A__PLUS(a__x(tt, 0), mark(tt)), A__X(mark(tt), mark(0)), MARK(tt)) A__X(0, s(0)) -> c7(A__PLUS(a__x(0, 0), mark(0)), A__X(mark(0), mark(0)), MARK(0)) A__X(s(z0), s(0)) -> c7(A__PLUS(a__x(s(mark(z0)), 0), mark(s(z0))), A__X(mark(s(z0)), mark(0)), MARK(s(z0))) A__X(x0, s(0)) -> c7(A__X(mark(x0), mark(0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c4_2 ---------------------------------------- (249) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (250) 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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) 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A__PLUS(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) A__X(x(x0, x1), s(x2)) -> c7(A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(s(s(z0)), s(x1)) -> c7(A__PLUS(a__x(mark(s(s(z0))), mark(x1)), s(s(mark(z0)))), A__X(mark(s(s(z0))), mark(x1)), MARK(s(s(z0)))) A__X(s(and(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(and(z0, z1))), mark(x1)), s(a__and(mark(z0), z1))), A__X(mark(s(and(z0, z1))), mark(x1)), MARK(s(and(z0, z1)))) A__X(s(plus(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(plus(z0, z1))), mark(x1)), s(a__plus(mark(z0), mark(z1)))), A__X(mark(s(plus(z0, z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__X(s(x(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(x(z0, z1))), mark(x1)), s(a__x(mark(z0), mark(z1)))), A__X(mark(s(x(z0, z1))), mark(x1)), MARK(s(x(z0, z1)))) A__X(s(tt), s(x1)) -> c7(A__PLUS(a__x(mark(s(tt)), mark(x1)), s(tt)), A__X(mark(s(tt)), mark(x1)), MARK(s(tt))) A__X(s(0), s(x1)) -> c7(A__PLUS(a__x(mark(s(0)), mark(x1)), s(0)), A__X(mark(s(0)), mark(x1)), MARK(s(0))) A__X(s(x0), s(x1)) -> c7(A__PLUS(x(mark(s(x0)), mark(x1)), s(mark(x0))), A__X(mark(s(x0)), mark(x1)), MARK(s(x0))) A__X(s(x0), s(s(z0))) -> c7(A__PLUS(a__x(mark(s(x0)), s(mark(z0))), s(mark(x0))), A__X(mark(s(x0)), mark(s(z0))), MARK(s(x0))) A__X(s(x0), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__and(mark(z0), z1)), s(mark(x0))), A__X(mark(s(x0)), mark(and(z0, z1))), MARK(s(x0))) A__X(s(x0), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__plus(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(plus(z0, z1))), MARK(s(x0))) A__X(s(x0), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__x(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(x(z0, z1))), MARK(s(x0))) A__X(s(x0), s(tt)) -> c7(A__PLUS(a__x(mark(s(x0)), tt), s(mark(x0))), A__X(mark(s(x0)), mark(tt)), MARK(s(x0))) A__X(s(x0), s(0)) -> c7(A__PLUS(a__x(mark(s(x0)), 0), s(mark(x0))), A__X(mark(s(x0)), mark(0)), MARK(s(x0))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(0, s(x1)) -> c7(A__PLUS(x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(x0, s(and(x1, z1))) -> c7(A__PLUS(a__x(mark(x0), and(mark(x1), z1)), mark(x0)), A__X(mark(x0), mark(and(x1, z1))), MARK(x0)) A__X(x0, s(and(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__and(mark(z0), z1), x2)), mark(x0)), A__X(mark(x0), mark(and(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(tt, x2)), mark(x0)), A__X(mark(x0), mark(and(tt, x2))), MARK(x0)) A__X(x0, s(and(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(0, x2)), mark(x0)), A__X(mark(x0), mark(and(0, x2))), MARK(x0)) A__X(x0, s(and(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(s(mark(z0)), x2)), mark(x0)), A__X(mark(x0), mark(and(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__and(mark(x1), x2)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(and(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(and(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(and(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(and(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__and(mark(x1), x2)), mark(s(z0))), A__X(mark(s(z0)), mark(and(x1, x2))), MARK(s(z0))) A__X(x0, s(and(x1, x2))) -> c7(A__X(mark(x0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__and(mark(x1), x2)), 0), A__X(mark(0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__PLUS(a__x(tt, a__and(mark(x1), x2)), mark(tt)), A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(0, a__and(mark(x1), x2)), mark(0)), A__X(mark(0), mark(and(x1, x2)))) A__X(x0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), plus(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x1, x2))), MARK(x0)) A__X(x0, s(plus(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(plus(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(plus(x1, tt))), MARK(x0)) A__X(x0, s(plus(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(plus(x1, 0))), MARK(x0)) A__X(x0, s(plus(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(plus(x1, s(z0)))), MARK(x0)) A__X(x0, s(plus(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(tt, x2))), MARK(x0)) A__X(x0, s(plus(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(0, x2))), MARK(x0)) A__X(x0, s(plus(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(plus(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(plus(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(plus(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(plus(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__plus(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(plus(x1, x2))), MARK(s(z0))) A__X(x0, s(plus(x1, x2))) -> c7(A__X(mark(x0), mark(plus(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__plus(mark(x1), mark(x2))), 0), A__X(mark(0), mark(plus(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__PLUS(a__x(tt, a__plus(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(0, a__plus(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(plus(x1, x2)))) A__X(x0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), x(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x1, x2))), MARK(x0)) A__X(x0, s(x(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(x(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(x(x1, tt))), MARK(x0)) A__X(x0, s(x(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(x(x1, 0))), MARK(x0)) A__X(x0, s(x(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(x(x1, s(z0)))), MARK(x0)) A__X(x0, s(x(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(tt, x2))), MARK(x0)) A__X(x0, s(x(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(0, x2))), MARK(x0)) A__X(x0, s(x(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(x(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__x(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(x(x1, x2))), MARK(s(z0))) A__X(x0, s(x(x1, x2))) -> c7(A__X(mark(x0), mark(x(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__X(mark(tt), mark(x(x1, x2)))) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__x(mark(x1), mark(x2))), 0), A__X(mark(0), mark(x(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__PLUS(a__x(tt, a__x(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(x(x1, x2)))) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(0, a__x(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(x(x1, x2)))) A__X(and(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), tt), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(tt)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), tt), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(tt)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), tt), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(tt)), MARK(x(z0, z1))) A__X(s(z0), s(tt)) -> c7(A__PLUS(a__x(s(mark(z0)), tt), mark(s(z0))), A__X(mark(s(z0)), mark(tt)), MARK(s(z0))) A__X(x0, s(tt)) -> c7(A__X(mark(x0), mark(tt))) A__X(tt, s(tt)) -> c7(A__X(mark(tt), mark(tt))) A__X(0, s(tt)) -> c7(A__PLUS(a__x(mark(0), tt), 0), A__X(mark(0), mark(tt))) A__X(tt, s(tt)) -> c7(A__PLUS(a__x(tt, tt), mark(tt)), A__X(mark(tt), mark(tt))) A__X(0, s(tt)) -> c7(A__PLUS(a__x(0, tt), mark(0)), A__X(mark(0), mark(tt))) A__X(x0, s(0)) -> c7(A__PLUS(0, mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(and(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), 0), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(0)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), 0), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(0)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), 0), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(0)), MARK(x(z0, z1))) A__X(s(z0), s(0)) -> c7(A__PLUS(a__x(s(mark(z0)), 0), mark(s(z0))), A__X(mark(s(z0)), mark(0)), MARK(s(z0))) A__X(x0, s(0)) -> c7(A__X(mark(x0), mark(0))) A__X(tt, s(0)) -> c7(A__X(mark(tt), mark(0))) A__X(0, s(0)) -> c7(A__PLUS(a__x(mark(0), 0), 0), A__X(mark(0), mark(0))) A__X(tt, s(0)) -> c7(A__PLUS(a__x(tt, 0), mark(tt)), A__X(mark(tt), mark(0))) A__X(0, s(0)) -> c7(A__PLUS(a__x(0, 0), mark(0)), A__X(mark(0), mark(0))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c18(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)) A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> 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A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), 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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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(mark(z0), mark(z1))), 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mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) A__X(x(x0, x1), s(x2)) -> c7(A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(s(s(z0)), s(x1)) -> c7(A__PLUS(a__x(mark(s(s(z0))), mark(x1)), s(s(mark(z0)))), A__X(mark(s(s(z0))), mark(x1)), MARK(s(s(z0)))) A__X(s(and(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(and(z0, z1))), mark(x1)), s(a__and(mark(z0), z1))), A__X(mark(s(and(z0, z1))), mark(x1)), MARK(s(and(z0, z1)))) A__X(s(plus(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(plus(z0, z1))), mark(x1)), s(a__plus(mark(z0), mark(z1)))), A__X(mark(s(plus(z0, z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__X(s(x(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(x(z0, z1))), mark(x1)), s(a__x(mark(z0), mark(z1)))), A__X(mark(s(x(z0, z1))), mark(x1)), MARK(s(x(z0, z1)))) A__X(s(tt), s(x1)) -> c7(A__PLUS(a__x(mark(s(tt)), mark(x1)), s(tt)), A__X(mark(s(tt)), mark(x1)), MARK(s(tt))) A__X(s(0), s(x1)) -> c7(A__PLUS(a__x(mark(s(0)), mark(x1)), s(0)), A__X(mark(s(0)), mark(x1)), MARK(s(0))) A__X(s(x0), s(x1)) -> c7(A__PLUS(x(mark(s(x0)), mark(x1)), s(mark(x0))), A__X(mark(s(x0)), mark(x1)), MARK(s(x0))) A__X(s(x0), s(s(z0))) -> c7(A__PLUS(a__x(mark(s(x0)), s(mark(z0))), s(mark(x0))), A__X(mark(s(x0)), mark(s(z0))), MARK(s(x0))) A__X(s(x0), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__and(mark(z0), z1)), s(mark(x0))), A__X(mark(s(x0)), mark(and(z0, z1))), MARK(s(x0))) A__X(s(x0), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__plus(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(plus(z0, z1))), MARK(s(x0))) A__X(s(x0), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__x(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(x(z0, z1))), MARK(s(x0))) A__X(s(x0), s(tt)) -> c7(A__PLUS(a__x(mark(s(x0)), tt), s(mark(x0))), A__X(mark(s(x0)), mark(tt)), MARK(s(x0))) A__X(s(x0), s(0)) -> c7(A__PLUS(a__x(mark(s(x0)), 0), s(mark(x0))), A__X(mark(s(x0)), mark(0)), MARK(s(x0))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(0, s(x1)) -> c7(A__PLUS(x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(x0, s(and(x1, z1))) -> c7(A__PLUS(a__x(mark(x0), and(mark(x1), z1)), mark(x0)), A__X(mark(x0), mark(and(x1, z1))), MARK(x0)) A__X(x0, s(and(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__and(mark(z0), z1), x2)), mark(x0)), A__X(mark(x0), mark(and(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(tt, x2)), mark(x0)), A__X(mark(x0), mark(and(tt, x2))), MARK(x0)) A__X(x0, s(and(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(0, x2)), mark(x0)), A__X(mark(x0), mark(and(0, x2))), MARK(x0)) A__X(x0, s(and(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(s(mark(z0)), x2)), mark(x0)), A__X(mark(x0), mark(and(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__and(mark(x1), x2)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(and(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(and(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(and(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(and(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__and(mark(x1), x2)), mark(s(z0))), A__X(mark(s(z0)), mark(and(x1, x2))), MARK(s(z0))) A__X(x0, s(and(x1, x2))) -> c7(A__X(mark(x0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__and(mark(x1), x2)), 0), A__X(mark(0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__PLUS(a__x(tt, a__and(mark(x1), x2)), mark(tt)), A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(0, a__and(mark(x1), x2)), mark(0)), A__X(mark(0), mark(and(x1, x2)))) A__X(x0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), plus(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x1, x2))), MARK(x0)) A__X(x0, s(plus(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(plus(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(plus(x1, tt))), MARK(x0)) A__X(x0, s(plus(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(plus(x1, 0))), MARK(x0)) A__X(x0, s(plus(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(plus(x1, s(z0)))), MARK(x0)) A__X(x0, s(plus(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(tt, x2))), MARK(x0)) A__X(x0, s(plus(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(0, x2))), MARK(x0)) A__X(x0, s(plus(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(plus(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(plus(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(plus(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(plus(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__plus(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(plus(x1, x2))), MARK(s(z0))) A__X(x0, s(plus(x1, x2))) -> c7(A__X(mark(x0), mark(plus(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__plus(mark(x1), mark(x2))), 0), A__X(mark(0), mark(plus(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__PLUS(a__x(tt, a__plus(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(0, a__plus(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(plus(x1, x2)))) A__X(x0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), x(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x1, x2))), MARK(x0)) A__X(x0, s(x(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(x(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(x(x1, tt))), MARK(x0)) A__X(x0, s(x(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(x(x1, 0))), MARK(x0)) A__X(x0, s(x(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(x(x1, s(z0)))), MARK(x0)) A__X(x0, s(x(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(tt, x2))), MARK(x0)) A__X(x0, s(x(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(0, x2))), MARK(x0)) A__X(x0, s(x(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(x(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__x(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(x(x1, x2))), MARK(s(z0))) A__X(x0, s(x(x1, x2))) -> c7(A__X(mark(x0), mark(x(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__X(mark(tt), mark(x(x1, x2)))) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__x(mark(x1), mark(x2))), 0), A__X(mark(0), mark(x(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__PLUS(a__x(tt, a__x(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(x(x1, x2)))) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(0, a__x(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(x(x1, x2)))) A__X(and(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), tt), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(tt)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), tt), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(tt)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), tt), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(tt)), MARK(x(z0, z1))) A__X(s(z0), s(tt)) -> c7(A__PLUS(a__x(s(mark(z0)), tt), mark(s(z0))), A__X(mark(s(z0)), mark(tt)), MARK(s(z0))) A__X(x0, s(tt)) -> c7(A__X(mark(x0), mark(tt))) A__X(tt, s(tt)) -> c7(A__X(mark(tt), mark(tt))) A__X(0, s(tt)) -> c7(A__PLUS(a__x(mark(0), tt), 0), A__X(mark(0), mark(tt))) A__X(tt, s(tt)) -> c7(A__PLUS(a__x(tt, tt), mark(tt)), A__X(mark(tt), mark(tt))) A__X(0, s(tt)) -> c7(A__PLUS(a__x(0, tt), mark(0)), A__X(mark(0), mark(tt))) A__X(x0, s(0)) -> c7(A__PLUS(0, mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(and(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), 0), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(0)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), 0), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(0)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), 0), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(0)), MARK(x(z0, z1))) A__X(s(z0), s(0)) -> c7(A__PLUS(a__x(s(mark(z0)), 0), mark(s(z0))), A__X(mark(s(z0)), mark(0)), MARK(s(z0))) A__X(x0, s(0)) -> c7(A__X(mark(x0), mark(0))) A__X(tt, s(0)) -> c7(A__X(mark(tt), mark(0))) A__X(0, s(0)) -> c7(A__PLUS(a__x(mark(0), 0), 0), A__X(mark(0), mark(0))) A__X(tt, s(0)) -> c7(A__PLUS(a__x(tt, 0), mark(tt)), A__X(mark(tt), mark(0))) A__X(0, s(0)) -> c7(A__PLUS(a__x(0, 0), mark(0)), A__X(mark(0), mark(0))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c4_2 ---------------------------------------- (251) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__X(x0, s(s(z0))) -> c7(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) by A__X(and(z0, z1), s(s(x1))) -> c7(A__PLUS(a__x(mark(and(z0, z1)), s(mark(x1))), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(s(x1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(s(x1))) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), s(mark(x1))), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(s(x1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(s(x1))) -> c7(A__PLUS(a__x(mark(x(z0, z1)), s(mark(x1))), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(s(x1))), MARK(x(z0, z1))) A__X(tt, s(s(x1))) -> c7(A__PLUS(a__x(mark(tt), s(mark(x1))), tt), A__X(mark(tt), mark(s(x1))), MARK(tt)) A__X(0, s(s(x1))) -> c7(A__PLUS(a__x(mark(0), s(mark(x1))), 0), A__X(mark(0), mark(s(x1))), MARK(0)) A__X(s(z0), s(s(x1))) -> c7(A__PLUS(a__x(mark(s(z0)), s(mark(x1))), s(mark(z0))), A__X(mark(s(z0)), mark(s(x1))), MARK(s(z0))) A__X(x0, s(s(x1))) -> c7(A__PLUS(a__plus(a__x(mark(mark(x0)), mark(mark(x1))), mark(mark(x0))), mark(x0)), A__X(mark(x0), mark(s(x1))), MARK(x0)) A__X(x0, s(s(x1))) -> c7(A__PLUS(x(mark(x0), s(mark(x1))), mark(x0)), A__X(mark(x0), mark(s(x1))), MARK(x0)) A__X(x0, s(s(and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), s(a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(s(and(z0, z1)))), MARK(x0)) A__X(x0, s(s(plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), s(a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(s(plus(z0, z1)))), MARK(x0)) A__X(x0, s(s(x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), s(a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(s(x(z0, z1)))), MARK(x0)) A__X(x0, s(s(tt))) -> c7(A__PLUS(a__x(mark(x0), s(tt)), mark(x0)), A__X(mark(x0), mark(s(tt))), MARK(x0)) A__X(x0, s(s(0))) -> c7(A__PLUS(a__x(mark(x0), s(0)), mark(x0)), A__X(mark(x0), mark(s(0))), MARK(x0)) A__X(x0, s(s(s(z0)))) -> c7(A__PLUS(a__x(mark(x0), s(s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(s(s(z0)))), MARK(x0)) A__X(and(z0, z1), s(s(x1))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), s(mark(x1))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(s(x1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(s(x1))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), s(mark(x1))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(s(x1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(s(x1))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), s(mark(x1))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(s(x1))), MARK(x(z0, z1))) A__X(tt, s(s(x1))) -> c7(A__PLUS(a__x(tt, s(mark(x1))), mark(tt)), A__X(mark(tt), mark(s(x1))), MARK(tt)) A__X(0, s(s(x1))) -> c7(A__PLUS(a__x(0, s(mark(x1))), mark(0)), A__X(mark(0), mark(s(x1))), MARK(0)) A__X(s(z0), s(s(x1))) -> c7(A__PLUS(a__x(s(mark(z0)), s(mark(x1))), mark(s(z0))), A__X(mark(s(z0)), mark(s(x1))), MARK(s(z0))) A__X(x0, s(s(x1))) -> c7(A__X(mark(x0), mark(s(x1)))) ---------------------------------------- (252) 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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 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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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> 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mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) A__X(x(x0, x1), s(x2)) -> c7(A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(s(s(z0)), s(x1)) -> c7(A__PLUS(a__x(mark(s(s(z0))), mark(x1)), s(s(mark(z0)))), A__X(mark(s(s(z0))), mark(x1)), MARK(s(s(z0)))) A__X(s(and(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(and(z0, z1))), mark(x1)), s(a__and(mark(z0), z1))), A__X(mark(s(and(z0, z1))), mark(x1)), MARK(s(and(z0, z1)))) A__X(s(plus(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(plus(z0, z1))), mark(x1)), s(a__plus(mark(z0), mark(z1)))), A__X(mark(s(plus(z0, z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__X(s(x(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(x(z0, z1))), mark(x1)), s(a__x(mark(z0), mark(z1)))), A__X(mark(s(x(z0, z1))), mark(x1)), MARK(s(x(z0, z1)))) A__X(s(tt), s(x1)) -> c7(A__PLUS(a__x(mark(s(tt)), mark(x1)), s(tt)), A__X(mark(s(tt)), mark(x1)), MARK(s(tt))) A__X(s(0), s(x1)) -> c7(A__PLUS(a__x(mark(s(0)), mark(x1)), s(0)), A__X(mark(s(0)), mark(x1)), MARK(s(0))) A__X(s(x0), s(x1)) -> c7(A__PLUS(x(mark(s(x0)), mark(x1)), s(mark(x0))), A__X(mark(s(x0)), mark(x1)), MARK(s(x0))) A__X(s(x0), s(s(z0))) -> c7(A__PLUS(a__x(mark(s(x0)), s(mark(z0))), s(mark(x0))), A__X(mark(s(x0)), mark(s(z0))), MARK(s(x0))) A__X(s(x0), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__and(mark(z0), z1)), s(mark(x0))), A__X(mark(s(x0)), mark(and(z0, z1))), MARK(s(x0))) A__X(s(x0), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__plus(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(plus(z0, z1))), MARK(s(x0))) A__X(s(x0), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__x(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(x(z0, z1))), MARK(s(x0))) A__X(s(x0), s(tt)) -> c7(A__PLUS(a__x(mark(s(x0)), tt), s(mark(x0))), A__X(mark(s(x0)), mark(tt)), MARK(s(x0))) A__X(s(x0), s(0)) -> c7(A__PLUS(a__x(mark(s(x0)), 0), s(mark(x0))), A__X(mark(s(x0)), mark(0)), MARK(s(x0))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(0, s(x1)) -> c7(A__PLUS(x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(x0, s(and(x1, z1))) -> c7(A__PLUS(a__x(mark(x0), and(mark(x1), z1)), mark(x0)), A__X(mark(x0), mark(and(x1, z1))), MARK(x0)) A__X(x0, s(and(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__and(mark(z0), z1), x2)), mark(x0)), A__X(mark(x0), mark(and(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(tt, x2)), mark(x0)), A__X(mark(x0), mark(and(tt, x2))), MARK(x0)) A__X(x0, s(and(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(0, x2)), mark(x0)), A__X(mark(x0), mark(and(0, x2))), MARK(x0)) A__X(x0, s(and(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(s(mark(z0)), x2)), mark(x0)), A__X(mark(x0), mark(and(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__and(mark(x1), x2)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(and(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(and(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(and(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(and(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__and(mark(x1), x2)), mark(s(z0))), A__X(mark(s(z0)), mark(and(x1, x2))), MARK(s(z0))) A__X(x0, s(and(x1, x2))) -> c7(A__X(mark(x0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__and(mark(x1), x2)), 0), A__X(mark(0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__PLUS(a__x(tt, a__and(mark(x1), x2)), mark(tt)), A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(0, a__and(mark(x1), x2)), mark(0)), A__X(mark(0), mark(and(x1, x2)))) A__X(x0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), plus(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x1, x2))), MARK(x0)) A__X(x0, s(plus(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(plus(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(plus(x1, tt))), MARK(x0)) A__X(x0, s(plus(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(plus(x1, 0))), MARK(x0)) A__X(x0, s(plus(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(plus(x1, s(z0)))), MARK(x0)) A__X(x0, s(plus(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(tt, x2))), MARK(x0)) A__X(x0, s(plus(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(0, x2))), MARK(x0)) A__X(x0, s(plus(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(plus(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(plus(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(plus(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(plus(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__plus(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(plus(x1, x2))), MARK(s(z0))) A__X(x0, s(plus(x1, x2))) -> c7(A__X(mark(x0), mark(plus(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__plus(mark(x1), mark(x2))), 0), A__X(mark(0), mark(plus(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__PLUS(a__x(tt, a__plus(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(0, a__plus(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(plus(x1, x2)))) A__X(x0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), x(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x1, x2))), MARK(x0)) A__X(x0, s(x(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(x(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(x(x1, tt))), MARK(x0)) A__X(x0, s(x(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(x(x1, 0))), MARK(x0)) A__X(x0, s(x(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(x(x1, s(z0)))), MARK(x0)) A__X(x0, s(x(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(tt, x2))), MARK(x0)) A__X(x0, s(x(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(0, x2))), MARK(x0)) A__X(x0, s(x(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(x(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__x(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(x(x1, x2))), MARK(s(z0))) A__X(x0, s(x(x1, x2))) -> c7(A__X(mark(x0), mark(x(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__X(mark(tt), mark(x(x1, x2)))) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__x(mark(x1), mark(x2))), 0), A__X(mark(0), mark(x(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__PLUS(a__x(tt, a__x(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(x(x1, x2)))) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(0, a__x(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(x(x1, x2)))) A__X(and(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), tt), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(tt)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), tt), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(tt)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), tt), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(tt)), MARK(x(z0, z1))) A__X(s(z0), s(tt)) -> c7(A__PLUS(a__x(s(mark(z0)), tt), mark(s(z0))), A__X(mark(s(z0)), mark(tt)), MARK(s(z0))) A__X(x0, s(tt)) -> c7(A__X(mark(x0), mark(tt))) A__X(tt, s(tt)) -> c7(A__X(mark(tt), mark(tt))) A__X(0, s(tt)) -> c7(A__PLUS(a__x(mark(0), tt), 0), A__X(mark(0), mark(tt))) A__X(tt, s(tt)) -> c7(A__PLUS(a__x(tt, tt), mark(tt)), A__X(mark(tt), mark(tt))) A__X(0, s(tt)) -> c7(A__PLUS(a__x(0, tt), mark(0)), A__X(mark(0), mark(tt))) A__X(x0, s(0)) -> c7(A__PLUS(0, mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(and(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), 0), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(0)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), 0), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(0)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), 0), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(0)), MARK(x(z0, z1))) A__X(s(z0), s(0)) -> c7(A__PLUS(a__x(s(mark(z0)), 0), mark(s(z0))), A__X(mark(s(z0)), mark(0)), MARK(s(z0))) A__X(x0, s(0)) -> c7(A__X(mark(x0), mark(0))) A__X(tt, s(0)) -> c7(A__X(mark(tt), mark(0))) A__X(0, s(0)) -> c7(A__PLUS(a__x(mark(0), 0), 0), A__X(mark(0), mark(0))) A__X(tt, s(0)) -> c7(A__PLUS(a__x(tt, 0), mark(tt)), A__X(mark(tt), mark(0))) A__X(0, s(0)) -> c7(A__PLUS(a__x(0, 0), mark(0)), A__X(mark(0), mark(0))) A__X(tt, s(s(x1))) -> c7(A__PLUS(a__x(mark(tt), s(mark(x1))), tt), A__X(mark(tt), mark(s(x1))), MARK(tt)) A__X(0, s(s(x1))) -> c7(A__PLUS(a__x(mark(0), s(mark(x1))), 0), A__X(mark(0), mark(s(x1))), MARK(0)) A__X(x0, s(s(x1))) -> c7(A__PLUS(a__plus(a__x(mark(mark(x0)), mark(mark(x1))), mark(mark(x0))), mark(x0)), A__X(mark(x0), mark(s(x1))), MARK(x0)) A__X(x0, s(s(and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), s(a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(s(and(z0, z1)))), MARK(x0)) A__X(x0, s(s(plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), s(a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(s(plus(z0, z1)))), MARK(x0)) A__X(x0, s(s(x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), s(a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(s(x(z0, z1)))), MARK(x0)) A__X(x0, s(s(tt))) -> c7(A__PLUS(a__x(mark(x0), s(tt)), mark(x0)), A__X(mark(x0), mark(s(tt))), MARK(x0)) A__X(x0, s(s(0))) -> c7(A__PLUS(a__x(mark(x0), s(0)), mark(x0)), A__X(mark(x0), mark(s(0))), MARK(x0)) A__X(x0, s(s(s(z0)))) -> c7(A__PLUS(a__x(mark(x0), s(s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(s(s(z0)))), MARK(x0)) A__X(and(z0, z1), s(s(x1))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), s(mark(x1))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(s(x1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(s(x1))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), s(mark(x1))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(s(x1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(s(x1))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), s(mark(x1))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(s(x1))), MARK(x(z0, z1))) A__X(tt, s(s(x1))) -> c7(A__PLUS(a__x(tt, s(mark(x1))), mark(tt)), A__X(mark(tt), mark(s(x1))), MARK(tt)) A__X(0, s(s(x1))) -> c7(A__PLUS(a__x(0, s(mark(x1))), mark(0)), A__X(mark(0), mark(s(x1))), MARK(0)) A__X(s(z0), s(s(x1))) -> c7(A__PLUS(a__x(s(mark(z0)), s(mark(x1))), mark(s(z0))), A__X(mark(s(z0)), mark(s(x1))), MARK(s(z0))) A__X(x0, s(s(x1))) -> c7(A__X(mark(x0), mark(s(x1)))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c18(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), 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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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), 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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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) A__X(x(x0, x1), s(x2)) -> c7(A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(s(s(z0)), s(x1)) -> c7(A__PLUS(a__x(mark(s(s(z0))), mark(x1)), s(s(mark(z0)))), A__X(mark(s(s(z0))), mark(x1)), MARK(s(s(z0)))) A__X(s(and(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(and(z0, z1))), mark(x1)), s(a__and(mark(z0), z1))), A__X(mark(s(and(z0, z1))), mark(x1)), MARK(s(and(z0, z1)))) A__X(s(plus(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(plus(z0, z1))), mark(x1)), s(a__plus(mark(z0), mark(z1)))), A__X(mark(s(plus(z0, z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__X(s(x(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(x(z0, z1))), mark(x1)), s(a__x(mark(z0), mark(z1)))), A__X(mark(s(x(z0, z1))), mark(x1)), MARK(s(x(z0, z1)))) A__X(s(tt), s(x1)) -> c7(A__PLUS(a__x(mark(s(tt)), mark(x1)), s(tt)), A__X(mark(s(tt)), mark(x1)), MARK(s(tt))) A__X(s(0), s(x1)) -> c7(A__PLUS(a__x(mark(s(0)), mark(x1)), s(0)), A__X(mark(s(0)), mark(x1)), MARK(s(0))) A__X(s(x0), s(x1)) -> c7(A__PLUS(x(mark(s(x0)), mark(x1)), s(mark(x0))), A__X(mark(s(x0)), mark(x1)), MARK(s(x0))) A__X(s(x0), s(s(z0))) -> c7(A__PLUS(a__x(mark(s(x0)), s(mark(z0))), s(mark(x0))), A__X(mark(s(x0)), mark(s(z0))), MARK(s(x0))) A__X(s(x0), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__and(mark(z0), z1)), s(mark(x0))), A__X(mark(s(x0)), mark(and(z0, z1))), MARK(s(x0))) A__X(s(x0), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__plus(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(plus(z0, z1))), MARK(s(x0))) A__X(s(x0), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__x(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(x(z0, z1))), MARK(s(x0))) A__X(s(x0), s(tt)) -> c7(A__PLUS(a__x(mark(s(x0)), tt), s(mark(x0))), A__X(mark(s(x0)), mark(tt)), MARK(s(x0))) A__X(s(x0), s(0)) -> c7(A__PLUS(a__x(mark(s(x0)), 0), s(mark(x0))), A__X(mark(s(x0)), mark(0)), MARK(s(x0))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(0, s(x1)) -> c7(A__PLUS(x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(x0, s(and(x1, z1))) -> c7(A__PLUS(a__x(mark(x0), and(mark(x1), z1)), mark(x0)), A__X(mark(x0), mark(and(x1, z1))), MARK(x0)) A__X(x0, s(and(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__and(mark(z0), z1), x2)), mark(x0)), A__X(mark(x0), mark(and(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(plus(z0, 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mark(plus(x1, x2))), MARK(x0)) A__X(x0, s(plus(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(plus(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(plus(x1, tt))), MARK(x0)) A__X(x0, s(plus(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(plus(x1, 0))), MARK(x0)) A__X(x0, s(plus(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(plus(x1, s(z0)))), MARK(x0)) A__X(x0, s(plus(and(z0, 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mark(tt)), A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(0, a__plus(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(plus(x1, x2)))) A__X(x0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), x(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x1, x2))), MARK(x0)) A__X(x0, s(x(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(x(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(x(x1, tt))), MARK(x0)) A__X(x0, s(x(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), 0)), 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a__x(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(x(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__x(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(x(x1, x2))), MARK(s(z0))) A__X(x0, s(x(x1, x2))) -> c7(A__X(mark(x0), mark(x(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__X(mark(tt), mark(x(x1, x2)))) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__x(mark(x1), mark(x2))), 0), A__X(mark(0), mark(x(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__PLUS(a__x(tt, a__x(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(x(x1, x2)))) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(0, a__x(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(x(x1, x2)))) A__X(and(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), tt), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(tt)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), tt), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(tt)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), tt), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(tt)), MARK(x(z0, z1))) A__X(s(z0), s(tt)) -> c7(A__PLUS(a__x(s(mark(z0)), tt), mark(s(z0))), A__X(mark(s(z0)), mark(tt)), MARK(s(z0))) A__X(x0, s(tt)) -> c7(A__X(mark(x0), mark(tt))) A__X(tt, s(tt)) -> c7(A__X(mark(tt), mark(tt))) A__X(0, s(tt)) -> c7(A__PLUS(a__x(mark(0), tt), 0), A__X(mark(0), mark(tt))) A__X(tt, s(tt)) -> c7(A__PLUS(a__x(tt, tt), mark(tt)), A__X(mark(tt), mark(tt))) A__X(0, s(tt)) -> c7(A__PLUS(a__x(0, tt), mark(0)), A__X(mark(0), mark(tt))) A__X(x0, s(0)) -> c7(A__PLUS(0, mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(and(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), 0), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(0)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), 0), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(0)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), 0), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(0)), MARK(x(z0, z1))) A__X(s(z0), s(0)) -> c7(A__PLUS(a__x(s(mark(z0)), 0), mark(s(z0))), A__X(mark(s(z0)), mark(0)), MARK(s(z0))) A__X(x0, s(0)) -> c7(A__X(mark(x0), mark(0))) A__X(tt, s(0)) -> c7(A__X(mark(tt), mark(0))) A__X(0, s(0)) -> c7(A__PLUS(a__x(mark(0), 0), 0), A__X(mark(0), mark(0))) A__X(tt, s(0)) -> c7(A__PLUS(a__x(tt, 0), mark(tt)), A__X(mark(tt), mark(0))) A__X(0, s(0)) -> c7(A__PLUS(a__x(0, 0), mark(0)), A__X(mark(0), mark(0))) A__X(tt, s(s(x1))) -> c7(A__PLUS(a__x(mark(tt), s(mark(x1))), tt), A__X(mark(tt), mark(s(x1))), MARK(tt)) A__X(0, s(s(x1))) -> c7(A__PLUS(a__x(mark(0), s(mark(x1))), 0), A__X(mark(0), mark(s(x1))), MARK(0)) A__X(x0, s(s(x1))) -> c7(A__PLUS(a__plus(a__x(mark(mark(x0)), mark(mark(x1))), mark(mark(x0))), mark(x0)), A__X(mark(x0), mark(s(x1))), MARK(x0)) A__X(x0, s(s(and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), s(a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(s(and(z0, z1)))), MARK(x0)) A__X(x0, s(s(plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), s(a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(s(plus(z0, z1)))), MARK(x0)) A__X(x0, s(s(x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), s(a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(s(x(z0, z1)))), MARK(x0)) A__X(x0, s(s(tt))) -> c7(A__PLUS(a__x(mark(x0), s(tt)), mark(x0)), A__X(mark(x0), mark(s(tt))), MARK(x0)) A__X(x0, s(s(0))) -> c7(A__PLUS(a__x(mark(x0), s(0)), mark(x0)), A__X(mark(x0), mark(s(0))), MARK(x0)) A__X(x0, s(s(s(z0)))) -> c7(A__PLUS(a__x(mark(x0), s(s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(s(s(z0)))), MARK(x0)) A__X(and(z0, z1), s(s(x1))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), s(mark(x1))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(s(x1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(s(x1))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), s(mark(x1))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(s(x1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(s(x1))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), s(mark(x1))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(s(x1))), MARK(x(z0, z1))) A__X(tt, s(s(x1))) -> c7(A__PLUS(a__x(tt, s(mark(x1))), mark(tt)), A__X(mark(tt), mark(s(x1))), MARK(tt)) A__X(0, s(s(x1))) -> c7(A__PLUS(a__x(0, s(mark(x1))), mark(0)), A__X(mark(0), mark(s(x1))), MARK(0)) A__X(s(z0), s(s(x1))) -> c7(A__PLUS(a__x(s(mark(z0)), s(mark(x1))), mark(s(z0))), A__X(mark(s(z0)), mark(s(x1))), MARK(s(z0))) A__X(x0, s(s(x1))) -> c7(A__X(mark(x0), mark(s(x1)))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c4_2 ---------------------------------------- (253) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (254) 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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), 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MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), MARK(and(x(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(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(plus(x1, x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) A__X(x(x0, x1), s(x2)) -> c7(A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(s(s(z0)), s(x1)) -> c7(A__PLUS(a__x(mark(s(s(z0))), mark(x1)), s(s(mark(z0)))), A__X(mark(s(s(z0))), mark(x1)), MARK(s(s(z0)))) A__X(s(and(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(and(z0, z1))), mark(x1)), s(a__and(mark(z0), z1))), A__X(mark(s(and(z0, z1))), mark(x1)), MARK(s(and(z0, z1)))) A__X(s(plus(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(plus(z0, z1))), mark(x1)), s(a__plus(mark(z0), mark(z1)))), A__X(mark(s(plus(z0, z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__X(s(x(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(x(z0, z1))), mark(x1)), s(a__x(mark(z0), mark(z1)))), A__X(mark(s(x(z0, z1))), mark(x1)), MARK(s(x(z0, z1)))) A__X(s(tt), s(x1)) -> c7(A__PLUS(a__x(mark(s(tt)), mark(x1)), s(tt)), A__X(mark(s(tt)), mark(x1)), MARK(s(tt))) A__X(s(0), s(x1)) -> c7(A__PLUS(a__x(mark(s(0)), mark(x1)), s(0)), A__X(mark(s(0)), mark(x1)), MARK(s(0))) A__X(s(x0), s(x1)) -> c7(A__PLUS(x(mark(s(x0)), mark(x1)), s(mark(x0))), A__X(mark(s(x0)), mark(x1)), MARK(s(x0))) A__X(s(x0), s(s(z0))) -> c7(A__PLUS(a__x(mark(s(x0)), s(mark(z0))), s(mark(x0))), A__X(mark(s(x0)), mark(s(z0))), MARK(s(x0))) A__X(s(x0), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__and(mark(z0), z1)), s(mark(x0))), A__X(mark(s(x0)), mark(and(z0, z1))), MARK(s(x0))) A__X(s(x0), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__plus(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(plus(z0, z1))), MARK(s(x0))) A__X(s(x0), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__x(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(x(z0, z1))), MARK(s(x0))) A__X(s(x0), s(tt)) -> c7(A__PLUS(a__x(mark(s(x0)), tt), s(mark(x0))), A__X(mark(s(x0)), mark(tt)), MARK(s(x0))) A__X(s(x0), s(0)) -> c7(A__PLUS(a__x(mark(s(x0)), 0), s(mark(x0))), A__X(mark(s(x0)), mark(0)), MARK(s(x0))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(0, s(x1)) -> c7(A__PLUS(x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(x0, s(and(x1, z1))) -> c7(A__PLUS(a__x(mark(x0), and(mark(x1), z1)), mark(x0)), A__X(mark(x0), mark(and(x1, z1))), MARK(x0)) A__X(x0, s(and(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__and(mark(z0), z1), x2)), mark(x0)), A__X(mark(x0), mark(and(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(tt, x2)), mark(x0)), A__X(mark(x0), mark(and(tt, x2))), MARK(x0)) A__X(x0, s(and(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(0, x2)), mark(x0)), A__X(mark(x0), mark(and(0, x2))), MARK(x0)) A__X(x0, s(and(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(s(mark(z0)), x2)), mark(x0)), A__X(mark(x0), mark(and(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__and(mark(x1), x2)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(and(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(and(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(and(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(and(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__and(mark(x1), x2)), mark(s(z0))), A__X(mark(s(z0)), mark(and(x1, x2))), MARK(s(z0))) A__X(x0, s(and(x1, x2))) -> c7(A__X(mark(x0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__and(mark(x1), x2)), 0), A__X(mark(0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__PLUS(a__x(tt, a__and(mark(x1), x2)), mark(tt)), A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(0, a__and(mark(x1), x2)), mark(0)), A__X(mark(0), mark(and(x1, x2)))) A__X(x0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), plus(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x1, x2))), MARK(x0)) A__X(x0, s(plus(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(plus(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(plus(x1, tt))), MARK(x0)) A__X(x0, s(plus(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(plus(x1, 0))), MARK(x0)) A__X(x0, s(plus(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(plus(x1, s(z0)))), MARK(x0)) A__X(x0, s(plus(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(tt, x2))), MARK(x0)) A__X(x0, s(plus(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(0, x2))), MARK(x0)) A__X(x0, s(plus(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(plus(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(plus(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(plus(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(plus(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__plus(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(plus(x1, x2))), MARK(s(z0))) A__X(x0, s(plus(x1, x2))) -> c7(A__X(mark(x0), mark(plus(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__plus(mark(x1), mark(x2))), 0), A__X(mark(0), mark(plus(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__PLUS(a__x(tt, a__plus(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(0, a__plus(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(plus(x1, x2)))) A__X(x0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), x(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x1, x2))), MARK(x0)) A__X(x0, s(x(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(x(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(x(x1, tt))), MARK(x0)) A__X(x0, s(x(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(x(x1, 0))), MARK(x0)) A__X(x0, s(x(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(x(x1, s(z0)))), MARK(x0)) A__X(x0, s(x(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(tt, x2))), MARK(x0)) A__X(x0, s(x(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(0, x2))), MARK(x0)) A__X(x0, s(x(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(x(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__x(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(x(x1, x2))), MARK(s(z0))) A__X(x0, s(x(x1, x2))) -> c7(A__X(mark(x0), mark(x(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__X(mark(tt), mark(x(x1, x2)))) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__x(mark(x1), mark(x2))), 0), A__X(mark(0), mark(x(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__PLUS(a__x(tt, a__x(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(x(x1, x2)))) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(0, a__x(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(x(x1, x2)))) A__X(and(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), tt), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(tt)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), tt), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(tt)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), tt), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(tt)), MARK(x(z0, z1))) A__X(s(z0), s(tt)) -> c7(A__PLUS(a__x(s(mark(z0)), tt), mark(s(z0))), A__X(mark(s(z0)), mark(tt)), MARK(s(z0))) A__X(x0, s(tt)) -> c7(A__X(mark(x0), mark(tt))) A__X(tt, s(tt)) -> c7(A__X(mark(tt), mark(tt))) A__X(0, s(tt)) -> c7(A__PLUS(a__x(mark(0), tt), 0), A__X(mark(0), mark(tt))) A__X(tt, s(tt)) -> c7(A__PLUS(a__x(tt, tt), mark(tt)), A__X(mark(tt), mark(tt))) A__X(0, s(tt)) -> c7(A__PLUS(a__x(0, tt), mark(0)), A__X(mark(0), mark(tt))) A__X(x0, s(0)) -> c7(A__PLUS(0, mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(and(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), 0), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(0)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), 0), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(0)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), 0), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(0)), MARK(x(z0, z1))) A__X(s(z0), s(0)) -> c7(A__PLUS(a__x(s(mark(z0)), 0), mark(s(z0))), A__X(mark(s(z0)), mark(0)), MARK(s(z0))) A__X(x0, s(0)) -> c7(A__X(mark(x0), mark(0))) A__X(tt, s(0)) -> c7(A__X(mark(tt), mark(0))) A__X(0, s(0)) -> c7(A__PLUS(a__x(mark(0), 0), 0), A__X(mark(0), mark(0))) A__X(tt, s(0)) -> c7(A__PLUS(a__x(tt, 0), mark(tt)), A__X(mark(tt), mark(0))) A__X(0, s(0)) -> c7(A__PLUS(a__x(0, 0), mark(0)), A__X(mark(0), mark(0))) A__X(x0, s(s(x1))) -> c7(A__PLUS(a__plus(a__x(mark(mark(x0)), mark(mark(x1))), mark(mark(x0))), mark(x0)), A__X(mark(x0), mark(s(x1))), MARK(x0)) A__X(x0, s(s(and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), s(a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(s(and(z0, z1)))), MARK(x0)) A__X(x0, s(s(plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), s(a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(s(plus(z0, z1)))), MARK(x0)) A__X(x0, s(s(x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), s(a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(s(x(z0, z1)))), MARK(x0)) A__X(x0, s(s(tt))) -> c7(A__PLUS(a__x(mark(x0), s(tt)), mark(x0)), A__X(mark(x0), mark(s(tt))), MARK(x0)) A__X(x0, s(s(0))) -> c7(A__PLUS(a__x(mark(x0), s(0)), mark(x0)), A__X(mark(x0), mark(s(0))), MARK(x0)) A__X(x0, s(s(s(z0)))) -> c7(A__PLUS(a__x(mark(x0), s(s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(s(s(z0)))), MARK(x0)) A__X(and(z0, z1), s(s(x1))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), s(mark(x1))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(s(x1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(s(x1))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), s(mark(x1))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(s(x1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(s(x1))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), s(mark(x1))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(s(x1))), MARK(x(z0, z1))) A__X(s(z0), s(s(x1))) -> c7(A__PLUS(a__x(s(mark(z0)), s(mark(x1))), mark(s(z0))), A__X(mark(s(z0)), mark(s(x1))), MARK(s(z0))) A__X(x0, s(s(x1))) -> c7(A__X(mark(x0), mark(s(x1)))) A__X(tt, s(s(x1))) -> c7(A__X(mark(tt), mark(s(x1)))) A__X(0, s(s(x1))) -> c7(A__PLUS(a__x(mark(0), s(mark(x1))), 0), A__X(mark(0), mark(s(x1)))) A__X(tt, s(s(x1))) -> c7(A__PLUS(a__x(tt, s(mark(x1))), mark(tt)), A__X(mark(tt), mark(s(x1)))) A__X(0, s(s(x1))) -> c7(A__PLUS(a__x(0, s(mark(x1))), mark(0)), A__X(mark(0), mark(s(x1)))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c18(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)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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), 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s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> 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x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), 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c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) A__X(x(x0, x1), s(x2)) -> c7(A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(s(s(z0)), s(x1)) -> c7(A__PLUS(a__x(mark(s(s(z0))), mark(x1)), s(s(mark(z0)))), A__X(mark(s(s(z0))), mark(x1)), MARK(s(s(z0)))) A__X(s(and(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(and(z0, z1))), mark(x1)), s(a__and(mark(z0), z1))), A__X(mark(s(and(z0, z1))), mark(x1)), MARK(s(and(z0, z1)))) A__X(s(plus(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(plus(z0, z1))), mark(x1)), s(a__plus(mark(z0), mark(z1)))), A__X(mark(s(plus(z0, z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__X(s(x(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(x(z0, z1))), mark(x1)), s(a__x(mark(z0), mark(z1)))), A__X(mark(s(x(z0, z1))), mark(x1)), MARK(s(x(z0, z1)))) A__X(s(tt), s(x1)) -> c7(A__PLUS(a__x(mark(s(tt)), mark(x1)), s(tt)), A__X(mark(s(tt)), mark(x1)), MARK(s(tt))) A__X(s(0), s(x1)) -> c7(A__PLUS(a__x(mark(s(0)), mark(x1)), s(0)), A__X(mark(s(0)), mark(x1)), MARK(s(0))) A__X(s(x0), s(x1)) -> c7(A__PLUS(x(mark(s(x0)), mark(x1)), s(mark(x0))), A__X(mark(s(x0)), mark(x1)), MARK(s(x0))) A__X(s(x0), s(s(z0))) -> c7(A__PLUS(a__x(mark(s(x0)), s(mark(z0))), s(mark(x0))), A__X(mark(s(x0)), mark(s(z0))), MARK(s(x0))) A__X(s(x0), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__and(mark(z0), z1)), s(mark(x0))), A__X(mark(s(x0)), mark(and(z0, z1))), MARK(s(x0))) A__X(s(x0), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__plus(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(plus(z0, z1))), MARK(s(x0))) A__X(s(x0), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__x(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(x(z0, z1))), MARK(s(x0))) A__X(s(x0), s(tt)) -> c7(A__PLUS(a__x(mark(s(x0)), tt), s(mark(x0))), A__X(mark(s(x0)), mark(tt)), MARK(s(x0))) A__X(s(x0), s(0)) -> c7(A__PLUS(a__x(mark(s(x0)), 0), s(mark(x0))), A__X(mark(s(x0)), mark(0)), MARK(s(x0))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(0, s(x1)) -> c7(A__PLUS(x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(x0, s(and(x1, z1))) -> c7(A__PLUS(a__x(mark(x0), and(mark(x1), z1)), mark(x0)), A__X(mark(x0), mark(and(x1, z1))), MARK(x0)) A__X(x0, s(and(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__and(mark(z0), z1), x2)), mark(x0)), A__X(mark(x0), mark(and(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(tt, x2)), mark(x0)), A__X(mark(x0), mark(and(tt, x2))), MARK(x0)) A__X(x0, s(and(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(0, x2)), mark(x0)), A__X(mark(x0), mark(and(0, x2))), MARK(x0)) A__X(x0, s(and(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(s(mark(z0)), x2)), mark(x0)), A__X(mark(x0), mark(and(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__and(mark(x1), x2)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(and(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(and(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(and(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(and(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__and(mark(x1), x2)), mark(s(z0))), A__X(mark(s(z0)), mark(and(x1, x2))), MARK(s(z0))) A__X(x0, s(and(x1, x2))) -> c7(A__X(mark(x0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__and(mark(x1), x2)), 0), A__X(mark(0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__PLUS(a__x(tt, a__and(mark(x1), x2)), mark(tt)), A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(0, a__and(mark(x1), x2)), mark(0)), A__X(mark(0), mark(and(x1, x2)))) A__X(x0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), plus(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x1, x2))), MARK(x0)) A__X(x0, s(plus(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(plus(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(plus(x1, tt))), MARK(x0)) A__X(x0, s(plus(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(plus(x1, 0))), MARK(x0)) A__X(x0, s(plus(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(plus(x1, s(z0)))), MARK(x0)) A__X(x0, s(plus(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(tt, x2))), MARK(x0)) A__X(x0, s(plus(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(0, x2))), MARK(x0)) A__X(x0, s(plus(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(plus(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(plus(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(plus(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(plus(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__plus(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(plus(x1, x2))), MARK(s(z0))) A__X(x0, s(plus(x1, x2))) -> c7(A__X(mark(x0), mark(plus(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__plus(mark(x1), mark(x2))), 0), A__X(mark(0), mark(plus(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__PLUS(a__x(tt, a__plus(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(0, a__plus(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(plus(x1, x2)))) A__X(x0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), x(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x1, x2))), MARK(x0)) A__X(x0, s(x(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(x(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(x(x1, tt))), MARK(x0)) A__X(x0, s(x(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(x(x1, 0))), MARK(x0)) A__X(x0, s(x(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(x(x1, s(z0)))), MARK(x0)) A__X(x0, s(x(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(tt, x2))), MARK(x0)) A__X(x0, s(x(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(0, x2))), MARK(x0)) A__X(x0, s(x(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(x(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__x(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(x(x1, x2))), MARK(s(z0))) A__X(x0, s(x(x1, x2))) -> c7(A__X(mark(x0), mark(x(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__X(mark(tt), mark(x(x1, x2)))) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__x(mark(x1), mark(x2))), 0), A__X(mark(0), mark(x(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__PLUS(a__x(tt, a__x(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(x(x1, x2)))) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(0, a__x(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(x(x1, x2)))) A__X(and(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), tt), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(tt)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), tt), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(tt)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), tt), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(tt)), MARK(x(z0, z1))) A__X(s(z0), s(tt)) -> c7(A__PLUS(a__x(s(mark(z0)), tt), mark(s(z0))), A__X(mark(s(z0)), mark(tt)), MARK(s(z0))) A__X(x0, s(tt)) -> c7(A__X(mark(x0), mark(tt))) A__X(tt, s(tt)) -> c7(A__X(mark(tt), mark(tt))) A__X(0, s(tt)) -> c7(A__PLUS(a__x(mark(0), tt), 0), A__X(mark(0), mark(tt))) A__X(tt, s(tt)) -> c7(A__PLUS(a__x(tt, tt), mark(tt)), A__X(mark(tt), mark(tt))) A__X(0, s(tt)) -> c7(A__PLUS(a__x(0, tt), mark(0)), A__X(mark(0), mark(tt))) A__X(x0, s(0)) -> c7(A__PLUS(0, mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(and(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), 0), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(0)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), 0), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(0)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), 0), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(0)), MARK(x(z0, z1))) A__X(s(z0), s(0)) -> c7(A__PLUS(a__x(s(mark(z0)), 0), mark(s(z0))), A__X(mark(s(z0)), mark(0)), MARK(s(z0))) A__X(x0, s(0)) -> c7(A__X(mark(x0), mark(0))) A__X(tt, s(0)) -> c7(A__X(mark(tt), mark(0))) A__X(0, s(0)) -> c7(A__PLUS(a__x(mark(0), 0), 0), A__X(mark(0), mark(0))) A__X(tt, s(0)) -> c7(A__PLUS(a__x(tt, 0), mark(tt)), A__X(mark(tt), mark(0))) A__X(0, s(0)) -> c7(A__PLUS(a__x(0, 0), mark(0)), A__X(mark(0), mark(0))) A__X(x0, s(s(x1))) -> c7(A__PLUS(a__plus(a__x(mark(mark(x0)), mark(mark(x1))), mark(mark(x0))), mark(x0)), A__X(mark(x0), mark(s(x1))), MARK(x0)) A__X(x0, s(s(and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), s(a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(s(and(z0, z1)))), MARK(x0)) A__X(x0, s(s(plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), s(a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(s(plus(z0, z1)))), MARK(x0)) A__X(x0, s(s(x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), s(a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(s(x(z0, z1)))), MARK(x0)) A__X(x0, s(s(tt))) -> c7(A__PLUS(a__x(mark(x0), s(tt)), mark(x0)), A__X(mark(x0), mark(s(tt))), MARK(x0)) A__X(x0, s(s(0))) -> c7(A__PLUS(a__x(mark(x0), s(0)), mark(x0)), A__X(mark(x0), mark(s(0))), MARK(x0)) A__X(x0, s(s(s(z0)))) -> c7(A__PLUS(a__x(mark(x0), s(s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(s(s(z0)))), MARK(x0)) A__X(and(z0, z1), s(s(x1))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), s(mark(x1))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(s(x1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(s(x1))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), s(mark(x1))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(s(x1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(s(x1))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), s(mark(x1))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(s(x1))), MARK(x(z0, z1))) A__X(s(z0), s(s(x1))) -> c7(A__PLUS(a__x(s(mark(z0)), s(mark(x1))), mark(s(z0))), A__X(mark(s(z0)), mark(s(x1))), MARK(s(z0))) A__X(x0, s(s(x1))) -> c7(A__X(mark(x0), mark(s(x1)))) A__X(tt, s(s(x1))) -> c7(A__X(mark(tt), mark(s(x1)))) A__X(0, s(s(x1))) -> c7(A__PLUS(a__x(mark(0), s(mark(x1))), 0), A__X(mark(0), mark(s(x1)))) A__X(tt, s(s(x1))) -> c7(A__PLUS(a__x(tt, s(mark(x1))), mark(tt)), A__X(mark(tt), mark(s(x1)))) A__X(0, s(s(x1))) -> c7(A__PLUS(a__x(0, s(mark(x1))), mark(0)), A__X(mark(0), mark(s(x1)))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c4_2 ---------------------------------------- (255) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) by A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(a__and(mark(x0), x1), mark(x2)), mark(and(x0, x1))), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(a__and(mark(x0), x1), a__and(mark(z0), z1)), mark(and(x0, x1))), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(a__and(mark(x0), x1), a__plus(mark(z0), mark(z1))), mark(and(x0, x1))), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(a__and(mark(x0), x1), a__x(mark(z0), mark(z1))), mark(and(x0, x1))), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(a__and(mark(x0), x1), tt), mark(and(x0, x1))), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(a__and(mark(x0), x1), 0), mark(and(x0, x1))), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(a__and(mark(x0), x1), s(mark(z0))), mark(and(x0, x1))), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(x0, z1), s(x2)) -> c7(A__PLUS(a__x(and(mark(x0), z1), mark(x2)), mark(and(x0, z1))), A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(a__and(a__and(mark(z0), z1), x1), mark(x2)), mark(and(and(z0, z1), x1))), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), mark(and(plus(z0, z1), x1))), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), mark(and(x(z0, z1), x1))), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(a__and(tt, x1), mark(x2)), mark(and(tt, x1))), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(a__and(0, x1), mark(x2)), mark(and(0, x1))), A__X(mark(and(0, x1)), mark(x2)), MARK(and(0, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(a__and(s(mark(z0)), x1), mark(x2)), mark(and(s(z0), x1))), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) ---------------------------------------- (256) 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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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)) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c14(A__X(0, mark(x1))) MARK(x(x0, and(z0, z1))) -> c15(A__X(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(x(x0, plus(z0, z1))) -> c15(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, x(z0, z1))) -> c15(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c15(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(and(z0, z1), x1)) -> c15(A__X(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c15(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c15(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c15(A__X(tt, mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c15(A__X(0, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c15(A__X(s(mark(z0)), mark(x1)), MARK(x1)) 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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__and(a__x(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(x(z0, z1), s(and(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(x(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, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__plus(mark(x1), a__x(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(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__plus(a__x(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(x(z0, z1), s(plus(x1, x2))) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(x(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(x(x1, and(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x0)) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x0)) A__PLUS(x0, s(x(x1, tt))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x0)) A__PLUS(x0, s(x(x1, 0))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x0)) A__PLUS(x0, s(x(x1, s(z0)))) -> c3(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x0)) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c3(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x0)) A__PLUS(x0, s(x(tt, x2))) -> c3(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(0, x2))) -> c3(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x0)) A__PLUS(x0, s(x(s(z0), 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A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) A__X(x(x0, x1), s(x2)) -> c7(A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(s(s(z0)), s(x1)) -> c7(A__PLUS(a__x(mark(s(s(z0))), mark(x1)), s(s(mark(z0)))), A__X(mark(s(s(z0))), mark(x1)), MARK(s(s(z0)))) A__X(s(and(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(and(z0, z1))), mark(x1)), s(a__and(mark(z0), z1))), A__X(mark(s(and(z0, z1))), mark(x1)), MARK(s(and(z0, z1)))) A__X(s(plus(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(plus(z0, z1))), mark(x1)), s(a__plus(mark(z0), mark(z1)))), A__X(mark(s(plus(z0, z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__X(s(x(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(x(z0, z1))), mark(x1)), s(a__x(mark(z0), mark(z1)))), A__X(mark(s(x(z0, z1))), mark(x1)), MARK(s(x(z0, z1)))) A__X(s(tt), s(x1)) -> c7(A__PLUS(a__x(mark(s(tt)), mark(x1)), s(tt)), A__X(mark(s(tt)), mark(x1)), MARK(s(tt))) A__X(s(0), s(x1)) -> c7(A__PLUS(a__x(mark(s(0)), mark(x1)), s(0)), A__X(mark(s(0)), mark(x1)), MARK(s(0))) A__X(s(x0), s(x1)) -> c7(A__PLUS(x(mark(s(x0)), mark(x1)), s(mark(x0))), A__X(mark(s(x0)), mark(x1)), MARK(s(x0))) A__X(s(x0), s(s(z0))) -> c7(A__PLUS(a__x(mark(s(x0)), s(mark(z0))), s(mark(x0))), A__X(mark(s(x0)), mark(s(z0))), MARK(s(x0))) A__X(s(x0), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__and(mark(z0), z1)), s(mark(x0))), A__X(mark(s(x0)), mark(and(z0, z1))), MARK(s(x0))) A__X(s(x0), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__plus(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(plus(z0, z1))), MARK(s(x0))) A__X(s(x0), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__x(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(x(z0, z1))), MARK(s(x0))) A__X(s(x0), s(tt)) -> c7(A__PLUS(a__x(mark(s(x0)), tt), s(mark(x0))), A__X(mark(s(x0)), mark(tt)), MARK(s(x0))) A__X(s(x0), s(0)) -> c7(A__PLUS(a__x(mark(s(x0)), 0), s(mark(x0))), A__X(mark(s(x0)), mark(0)), MARK(s(x0))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(0, s(x1)) -> c7(A__PLUS(x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(x0, s(and(x1, z1))) -> c7(A__PLUS(a__x(mark(x0), and(mark(x1), z1)), mark(x0)), A__X(mark(x0), mark(and(x1, z1))), MARK(x0)) A__X(x0, s(and(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__and(mark(z0), z1), x2)), mark(x0)), A__X(mark(x0), mark(and(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(tt, x2)), mark(x0)), A__X(mark(x0), mark(and(tt, x2))), MARK(x0)) A__X(x0, s(and(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(0, x2)), mark(x0)), A__X(mark(x0), mark(and(0, x2))), MARK(x0)) A__X(x0, s(and(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(s(mark(z0)), x2)), mark(x0)), A__X(mark(x0), mark(and(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__and(mark(x1), x2)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(and(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(and(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(and(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(and(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__and(mark(x1), x2)), mark(s(z0))), A__X(mark(s(z0)), mark(and(x1, x2))), MARK(s(z0))) A__X(x0, s(and(x1, x2))) -> c7(A__X(mark(x0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__and(mark(x1), x2)), 0), A__X(mark(0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__PLUS(a__x(tt, a__and(mark(x1), x2)), mark(tt)), A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(0, a__and(mark(x1), x2)), mark(0)), A__X(mark(0), mark(and(x1, x2)))) A__X(x0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), plus(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x1, x2))), MARK(x0)) A__X(x0, s(plus(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(plus(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(plus(x1, tt))), MARK(x0)) A__X(x0, s(plus(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(plus(x1, 0))), MARK(x0)) A__X(x0, s(plus(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(plus(x1, s(z0)))), MARK(x0)) A__X(x0, s(plus(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(tt, x2))), MARK(x0)) A__X(x0, s(plus(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(0, x2))), MARK(x0)) A__X(x0, s(plus(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(plus(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(plus(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(plus(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(plus(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__plus(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(plus(x1, x2))), MARK(s(z0))) A__X(x0, s(plus(x1, x2))) -> c7(A__X(mark(x0), mark(plus(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__plus(mark(x1), mark(x2))), 0), A__X(mark(0), mark(plus(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__PLUS(a__x(tt, a__plus(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(0, a__plus(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(plus(x1, x2)))) A__X(x0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), x(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x1, x2))), MARK(x0)) A__X(x0, s(x(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(x(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(x(x1, tt))), MARK(x0)) A__X(x0, s(x(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(x(x1, 0))), MARK(x0)) A__X(x0, s(x(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(x(x1, s(z0)))), MARK(x0)) A__X(x0, s(x(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(tt, x2))), MARK(x0)) A__X(x0, s(x(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(0, x2))), MARK(x0)) A__X(x0, s(x(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(x(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__x(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(x(x1, x2))), MARK(s(z0))) A__X(x0, s(x(x1, x2))) -> c7(A__X(mark(x0), mark(x(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__X(mark(tt), mark(x(x1, x2)))) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__x(mark(x1), mark(x2))), 0), A__X(mark(0), mark(x(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__PLUS(a__x(tt, a__x(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(x(x1, x2)))) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(0, a__x(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(x(x1, x2)))) A__X(and(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), tt), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(tt)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), tt), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(tt)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), tt), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(tt)), MARK(x(z0, z1))) A__X(s(z0), s(tt)) -> c7(A__PLUS(a__x(s(mark(z0)), tt), mark(s(z0))), A__X(mark(s(z0)), mark(tt)), MARK(s(z0))) A__X(x0, s(tt)) -> c7(A__X(mark(x0), mark(tt))) A__X(tt, s(tt)) -> c7(A__X(mark(tt), mark(tt))) A__X(0, s(tt)) -> c7(A__PLUS(a__x(mark(0), tt), 0), A__X(mark(0), mark(tt))) A__X(tt, s(tt)) -> c7(A__PLUS(a__x(tt, tt), mark(tt)), A__X(mark(tt), mark(tt))) A__X(0, s(tt)) -> c7(A__PLUS(a__x(0, tt), mark(0)), A__X(mark(0), mark(tt))) A__X(x0, s(0)) -> c7(A__PLUS(0, mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(and(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), 0), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(0)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), 0), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(0)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), 0), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(0)), MARK(x(z0, z1))) A__X(s(z0), s(0)) -> c7(A__PLUS(a__x(s(mark(z0)), 0), mark(s(z0))), A__X(mark(s(z0)), mark(0)), MARK(s(z0))) A__X(x0, s(0)) -> c7(A__X(mark(x0), mark(0))) A__X(tt, s(0)) -> c7(A__X(mark(tt), mark(0))) A__X(0, s(0)) -> c7(A__PLUS(a__x(mark(0), 0), 0), A__X(mark(0), mark(0))) A__X(tt, s(0)) -> c7(A__PLUS(a__x(tt, 0), mark(tt)), A__X(mark(tt), mark(0))) A__X(0, s(0)) -> c7(A__PLUS(a__x(0, 0), mark(0)), A__X(mark(0), mark(0))) A__X(x0, s(s(x1))) -> c7(A__PLUS(a__plus(a__x(mark(mark(x0)), mark(mark(x1))), mark(mark(x0))), mark(x0)), A__X(mark(x0), mark(s(x1))), MARK(x0)) A__X(x0, s(s(and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), s(a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(s(and(z0, z1)))), MARK(x0)) A__X(x0, s(s(plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), s(a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(s(plus(z0, z1)))), MARK(x0)) A__X(x0, s(s(x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), s(a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(s(x(z0, z1)))), MARK(x0)) A__X(x0, s(s(tt))) -> c7(A__PLUS(a__x(mark(x0), s(tt)), mark(x0)), A__X(mark(x0), mark(s(tt))), MARK(x0)) A__X(x0, s(s(0))) -> c7(A__PLUS(a__x(mark(x0), s(0)), mark(x0)), A__X(mark(x0), mark(s(0))), MARK(x0)) A__X(x0, s(s(s(z0)))) -> c7(A__PLUS(a__x(mark(x0), s(s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(s(s(z0)))), MARK(x0)) A__X(and(z0, z1), s(s(x1))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), s(mark(x1))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(s(x1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(s(x1))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), s(mark(x1))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(s(x1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(s(x1))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), s(mark(x1))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(s(x1))), MARK(x(z0, z1))) A__X(s(z0), s(s(x1))) -> c7(A__PLUS(a__x(s(mark(z0)), s(mark(x1))), mark(s(z0))), A__X(mark(s(z0)), mark(s(x1))), MARK(s(z0))) A__X(x0, s(s(x1))) -> c7(A__X(mark(x0), mark(s(x1)))) A__X(tt, s(s(x1))) -> c7(A__X(mark(tt), mark(s(x1)))) A__X(0, s(s(x1))) -> c7(A__PLUS(a__x(mark(0), s(mark(x1))), 0), A__X(mark(0), mark(s(x1)))) A__X(tt, s(s(x1))) -> c7(A__PLUS(a__x(tt, s(mark(x1))), mark(tt)), A__X(mark(tt), mark(s(x1)))) A__X(0, s(s(x1))) -> c7(A__PLUS(a__x(0, s(mark(x1))), mark(0)), A__X(mark(0), mark(s(x1)))) A__X(and(x0, z1), s(x2)) -> c7(A__PLUS(a__x(and(mark(x0), z1), mark(x2)), mark(and(x0, z1))), A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(a__and(a__and(mark(z0), z1), x1), mark(x2)), mark(and(and(z0, z1), x1))), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), mark(and(plus(z0, z1), x1))), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), mark(and(x(z0, z1), x1))), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(a__and(tt, x1), mark(x2)), mark(and(tt, x1))), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(a__and(0, x1), mark(x2)), mark(and(0, x1))), A__X(mark(and(0, x1)), mark(x2)), MARK(and(0, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(a__and(s(mark(z0)), x1), mark(x2)), mark(and(s(z0), x1))), A__X(mark(and(s(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)) -> c18(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)) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), 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x2)), MARK(and(x1, x2))) A__PLUS(x(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__x(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, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), MARK(plus(x1, x(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(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) A__X(x(x0, x1), s(x2)) -> c7(A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(s(s(z0)), s(x1)) -> c7(A__PLUS(a__x(mark(s(s(z0))), mark(x1)), s(s(mark(z0)))), A__X(mark(s(s(z0))), mark(x1)), MARK(s(s(z0)))) A__X(s(and(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(and(z0, z1))), mark(x1)), s(a__and(mark(z0), z1))), A__X(mark(s(and(z0, z1))), mark(x1)), MARK(s(and(z0, z1)))) A__X(s(plus(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(plus(z0, z1))), mark(x1)), s(a__plus(mark(z0), mark(z1)))), A__X(mark(s(plus(z0, z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__X(s(x(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(x(z0, z1))), mark(x1)), s(a__x(mark(z0), mark(z1)))), A__X(mark(s(x(z0, z1))), mark(x1)), MARK(s(x(z0, z1)))) A__X(s(tt), s(x1)) -> c7(A__PLUS(a__x(mark(s(tt)), mark(x1)), s(tt)), A__X(mark(s(tt)), mark(x1)), MARK(s(tt))) A__X(s(0), s(x1)) -> c7(A__PLUS(a__x(mark(s(0)), mark(x1)), s(0)), A__X(mark(s(0)), mark(x1)), MARK(s(0))) A__X(s(x0), s(x1)) -> c7(A__PLUS(x(mark(s(x0)), mark(x1)), s(mark(x0))), A__X(mark(s(x0)), mark(x1)), MARK(s(x0))) A__X(s(x0), s(s(z0))) -> c7(A__PLUS(a__x(mark(s(x0)), s(mark(z0))), s(mark(x0))), A__X(mark(s(x0)), mark(s(z0))), MARK(s(x0))) A__X(s(x0), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__and(mark(z0), z1)), s(mark(x0))), A__X(mark(s(x0)), mark(and(z0, z1))), MARK(s(x0))) A__X(s(x0), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__plus(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(plus(z0, z1))), MARK(s(x0))) A__X(s(x0), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__x(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(x(z0, z1))), MARK(s(x0))) A__X(s(x0), s(tt)) -> c7(A__PLUS(a__x(mark(s(x0)), tt), s(mark(x0))), A__X(mark(s(x0)), mark(tt)), MARK(s(x0))) A__X(s(x0), s(0)) -> c7(A__PLUS(a__x(mark(s(x0)), 0), s(mark(x0))), A__X(mark(s(x0)), mark(0)), MARK(s(x0))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(0, s(x1)) -> c7(A__PLUS(x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(x0, s(and(x1, z1))) -> c7(A__PLUS(a__x(mark(x0), and(mark(x1), z1)), mark(x0)), A__X(mark(x0), mark(and(x1, z1))), MARK(x0)) A__X(x0, s(and(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__and(mark(z0), z1), x2)), mark(x0)), A__X(mark(x0), mark(and(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(tt, x2)), mark(x0)), A__X(mark(x0), mark(and(tt, x2))), MARK(x0)) A__X(x0, s(and(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(0, x2)), mark(x0)), A__X(mark(x0), mark(and(0, x2))), MARK(x0)) A__X(x0, s(and(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(s(mark(z0)), x2)), mark(x0)), A__X(mark(x0), mark(and(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__and(mark(x1), x2)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(and(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(and(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(and(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(and(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__and(mark(x1), x2)), mark(s(z0))), A__X(mark(s(z0)), mark(and(x1, x2))), MARK(s(z0))) A__X(x0, s(and(x1, x2))) -> c7(A__X(mark(x0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__and(mark(x1), x2)), 0), A__X(mark(0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__PLUS(a__x(tt, a__and(mark(x1), x2)), mark(tt)), A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(0, a__and(mark(x1), x2)), mark(0)), A__X(mark(0), mark(and(x1, x2)))) A__X(x0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), plus(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x1, x2))), MARK(x0)) A__X(x0, s(plus(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(plus(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(plus(x1, tt))), MARK(x0)) A__X(x0, s(plus(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(plus(x1, 0))), MARK(x0)) A__X(x0, s(plus(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(plus(x1, s(z0)))), MARK(x0)) A__X(x0, s(plus(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(tt, x2))), MARK(x0)) A__X(x0, s(plus(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(0, x2))), MARK(x0)) A__X(x0, s(plus(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(plus(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(plus(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(plus(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(plus(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__plus(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(plus(x1, x2))), MARK(s(z0))) A__X(x0, s(plus(x1, x2))) -> c7(A__X(mark(x0), mark(plus(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__plus(mark(x1), mark(x2))), 0), A__X(mark(0), mark(plus(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__PLUS(a__x(tt, a__plus(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(0, a__plus(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(plus(x1, x2)))) A__X(x0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), x(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x1, x2))), MARK(x0)) A__X(x0, s(x(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(x(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(x(x1, tt))), MARK(x0)) A__X(x0, s(x(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(x(x1, 0))), MARK(x0)) A__X(x0, s(x(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(x(x1, s(z0)))), MARK(x0)) A__X(x0, s(x(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(tt, x2))), MARK(x0)) A__X(x0, s(x(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(0, x2))), MARK(x0)) A__X(x0, s(x(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(x(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__x(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(x(x1, x2))), MARK(s(z0))) A__X(x0, s(x(x1, x2))) -> c7(A__X(mark(x0), mark(x(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__X(mark(tt), mark(x(x1, x2)))) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__x(mark(x1), mark(x2))), 0), A__X(mark(0), mark(x(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__PLUS(a__x(tt, a__x(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(x(x1, x2)))) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(0, a__x(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(x(x1, x2)))) A__X(and(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), tt), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(tt)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), tt), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(tt)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), tt), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(tt)), MARK(x(z0, z1))) A__X(s(z0), s(tt)) -> c7(A__PLUS(a__x(s(mark(z0)), tt), mark(s(z0))), A__X(mark(s(z0)), mark(tt)), MARK(s(z0))) A__X(x0, s(tt)) -> c7(A__X(mark(x0), mark(tt))) A__X(tt, s(tt)) -> c7(A__X(mark(tt), mark(tt))) A__X(0, s(tt)) -> c7(A__PLUS(a__x(mark(0), tt), 0), A__X(mark(0), mark(tt))) A__X(tt, s(tt)) -> c7(A__PLUS(a__x(tt, tt), mark(tt)), A__X(mark(tt), mark(tt))) A__X(0, s(tt)) -> c7(A__PLUS(a__x(0, tt), mark(0)), A__X(mark(0), mark(tt))) A__X(x0, s(0)) -> c7(A__PLUS(0, mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(and(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), 0), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(0)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), 0), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(0)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), 0), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(0)), MARK(x(z0, z1))) A__X(s(z0), s(0)) -> c7(A__PLUS(a__x(s(mark(z0)), 0), mark(s(z0))), A__X(mark(s(z0)), mark(0)), MARK(s(z0))) A__X(x0, s(0)) -> c7(A__X(mark(x0), mark(0))) A__X(tt, s(0)) -> c7(A__X(mark(tt), mark(0))) A__X(0, s(0)) -> c7(A__PLUS(a__x(mark(0), 0), 0), A__X(mark(0), mark(0))) A__X(tt, s(0)) -> c7(A__PLUS(a__x(tt, 0), mark(tt)), A__X(mark(tt), mark(0))) A__X(0, s(0)) -> c7(A__PLUS(a__x(0, 0), mark(0)), A__X(mark(0), mark(0))) A__X(x0, s(s(x1))) -> c7(A__PLUS(a__plus(a__x(mark(mark(x0)), mark(mark(x1))), mark(mark(x0))), mark(x0)), A__X(mark(x0), mark(s(x1))), MARK(x0)) A__X(x0, s(s(and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), s(a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(s(and(z0, z1)))), MARK(x0)) A__X(x0, s(s(plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), s(a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(s(plus(z0, z1)))), MARK(x0)) A__X(x0, s(s(x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), s(a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(s(x(z0, z1)))), MARK(x0)) A__X(x0, s(s(tt))) -> c7(A__PLUS(a__x(mark(x0), s(tt)), mark(x0)), A__X(mark(x0), mark(s(tt))), MARK(x0)) A__X(x0, s(s(0))) -> c7(A__PLUS(a__x(mark(x0), s(0)), mark(x0)), A__X(mark(x0), mark(s(0))), MARK(x0)) A__X(x0, s(s(s(z0)))) -> c7(A__PLUS(a__x(mark(x0), s(s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(s(s(z0)))), MARK(x0)) A__X(and(z0, z1), s(s(x1))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), s(mark(x1))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(s(x1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(s(x1))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), s(mark(x1))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(s(x1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(s(x1))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), s(mark(x1))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(s(x1))), MARK(x(z0, z1))) A__X(s(z0), s(s(x1))) -> c7(A__PLUS(a__x(s(mark(z0)), s(mark(x1))), mark(s(z0))), A__X(mark(s(z0)), mark(s(x1))), MARK(s(z0))) A__X(x0, s(s(x1))) -> c7(A__X(mark(x0), mark(s(x1)))) A__X(tt, s(s(x1))) -> c7(A__X(mark(tt), mark(s(x1)))) A__X(0, s(s(x1))) -> c7(A__PLUS(a__x(mark(0), s(mark(x1))), 0), A__X(mark(0), mark(s(x1)))) A__X(tt, s(s(x1))) -> c7(A__PLUS(a__x(tt, s(mark(x1))), mark(tt)), A__X(mark(tt), mark(s(x1)))) A__X(0, s(s(x1))) -> c7(A__PLUS(a__x(0, s(mark(x1))), mark(0)), A__X(mark(0), mark(s(x1)))) A__X(and(x0, z1), s(x2)) -> c7(A__PLUS(a__x(and(mark(x0), z1), mark(x2)), mark(and(x0, z1))), A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(a__and(a__and(mark(z0), z1), x1), mark(x2)), mark(and(and(z0, z1), x1))), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), mark(and(plus(z0, z1), x1))), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), mark(and(x(z0, z1), x1))), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(a__and(tt, x1), mark(x2)), mark(and(tt, x1))), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(a__and(0, x1), mark(x2)), mark(and(0, x1))), A__X(mark(and(0, x1)), mark(x2)), MARK(and(0, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(a__and(s(mark(z0)), x1), mark(x2)), mark(and(s(z0), x1))), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c4_2 ---------------------------------------- (257) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (258) 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) a__x(z0, 0) -> 0 a__x(z0, s(z1)) -> a__plus(a__x(mark(z0), mark(z1)), mark(z0)) a__x(z0, z1) -> x(z0, z1) mark(and(z0, z1)) -> a__and(mark(z0), z1) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(x(z0, z1)) -> a__x(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)) -> c18(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)) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, 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MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) A__X(x(x0, x1), s(x2)) -> c7(A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(s(s(z0)), s(x1)) -> c7(A__PLUS(a__x(mark(s(s(z0))), mark(x1)), s(s(mark(z0)))), A__X(mark(s(s(z0))), mark(x1)), MARK(s(s(z0)))) A__X(s(and(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(and(z0, z1))), mark(x1)), s(a__and(mark(z0), z1))), A__X(mark(s(and(z0, z1))), mark(x1)), MARK(s(and(z0, z1)))) A__X(s(plus(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(plus(z0, z1))), mark(x1)), s(a__plus(mark(z0), mark(z1)))), A__X(mark(s(plus(z0, z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__X(s(x(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(x(z0, z1))), mark(x1)), s(a__x(mark(z0), mark(z1)))), A__X(mark(s(x(z0, z1))), mark(x1)), MARK(s(x(z0, z1)))) A__X(s(tt), s(x1)) -> c7(A__PLUS(a__x(mark(s(tt)), mark(x1)), s(tt)), A__X(mark(s(tt)), mark(x1)), MARK(s(tt))) A__X(s(0), s(x1)) -> c7(A__PLUS(a__x(mark(s(0)), mark(x1)), s(0)), A__X(mark(s(0)), mark(x1)), MARK(s(0))) A__X(s(x0), s(x1)) -> c7(A__PLUS(x(mark(s(x0)), mark(x1)), s(mark(x0))), A__X(mark(s(x0)), mark(x1)), MARK(s(x0))) A__X(s(x0), s(s(z0))) -> c7(A__PLUS(a__x(mark(s(x0)), s(mark(z0))), s(mark(x0))), A__X(mark(s(x0)), mark(s(z0))), MARK(s(x0))) A__X(s(x0), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__and(mark(z0), z1)), s(mark(x0))), A__X(mark(s(x0)), mark(and(z0, z1))), MARK(s(x0))) A__X(s(x0), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__plus(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(plus(z0, z1))), MARK(s(x0))) A__X(s(x0), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__x(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(x(z0, z1))), MARK(s(x0))) A__X(s(x0), s(tt)) -> c7(A__PLUS(a__x(mark(s(x0)), tt), s(mark(x0))), A__X(mark(s(x0)), mark(tt)), MARK(s(x0))) A__X(s(x0), s(0)) -> c7(A__PLUS(a__x(mark(s(x0)), 0), s(mark(x0))), A__X(mark(s(x0)), mark(0)), MARK(s(x0))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(0, s(x1)) -> c7(A__PLUS(x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(x0, s(and(x1, z1))) -> c7(A__PLUS(a__x(mark(x0), and(mark(x1), z1)), mark(x0)), A__X(mark(x0), mark(and(x1, z1))), MARK(x0)) A__X(x0, s(and(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__and(mark(z0), z1), x2)), mark(x0)), A__X(mark(x0), mark(and(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(plus(z0, 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mark(tt)), A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(0, a__plus(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(plus(x1, x2)))) A__X(x0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), x(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x1, x2))), MARK(x0)) A__X(x0, s(x(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(x(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(x(x1, tt))), MARK(x0)) A__X(x0, s(x(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(x(x1, 0))), MARK(x0)) A__X(x0, s(x(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(x(x1, s(z0)))), MARK(x0)) A__X(x0, s(x(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(tt, x2))), MARK(x0)) A__X(x0, s(x(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(0, x2))), MARK(x0)) A__X(x0, s(x(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(x(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__x(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(x(x1, x2))), MARK(s(z0))) A__X(x0, s(x(x1, x2))) -> c7(A__X(mark(x0), mark(x(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__X(mark(tt), mark(x(x1, x2)))) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__x(mark(x1), mark(x2))), 0), A__X(mark(0), mark(x(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__PLUS(a__x(tt, a__x(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(x(x1, x2)))) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(0, a__x(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(x(x1, x2)))) A__X(and(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), tt), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(tt)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), tt), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(tt)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), tt), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(tt)), MARK(x(z0, z1))) A__X(s(z0), s(tt)) -> c7(A__PLUS(a__x(s(mark(z0)), tt), mark(s(z0))), A__X(mark(s(z0)), mark(tt)), MARK(s(z0))) A__X(x0, s(tt)) -> c7(A__X(mark(x0), mark(tt))) A__X(tt, s(tt)) -> c7(A__X(mark(tt), mark(tt))) A__X(0, s(tt)) -> c7(A__PLUS(a__x(mark(0), tt), 0), A__X(mark(0), mark(tt))) A__X(tt, s(tt)) -> c7(A__PLUS(a__x(tt, tt), mark(tt)), A__X(mark(tt), mark(tt))) A__X(0, s(tt)) -> c7(A__PLUS(a__x(0, tt), mark(0)), A__X(mark(0), mark(tt))) A__X(x0, s(0)) -> c7(A__PLUS(0, mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(and(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), 0), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(0)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), 0), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(0)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), 0), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(0)), MARK(x(z0, z1))) A__X(s(z0), s(0)) -> c7(A__PLUS(a__x(s(mark(z0)), 0), mark(s(z0))), A__X(mark(s(z0)), mark(0)), MARK(s(z0))) A__X(x0, s(0)) -> c7(A__X(mark(x0), mark(0))) A__X(tt, s(0)) -> c7(A__X(mark(tt), mark(0))) A__X(0, s(0)) -> c7(A__PLUS(a__x(mark(0), 0), 0), A__X(mark(0), mark(0))) A__X(tt, s(0)) -> c7(A__PLUS(a__x(tt, 0), mark(tt)), A__X(mark(tt), mark(0))) A__X(0, s(0)) -> c7(A__PLUS(a__x(0, 0), mark(0)), A__X(mark(0), mark(0))) A__X(x0, s(s(x1))) -> c7(A__PLUS(a__plus(a__x(mark(mark(x0)), mark(mark(x1))), mark(mark(x0))), mark(x0)), A__X(mark(x0), mark(s(x1))), MARK(x0)) A__X(x0, s(s(and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), s(a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(s(and(z0, z1)))), MARK(x0)) A__X(x0, s(s(plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), s(a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(s(plus(z0, z1)))), MARK(x0)) A__X(x0, s(s(x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), s(a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(s(x(z0, z1)))), MARK(x0)) A__X(x0, s(s(tt))) -> c7(A__PLUS(a__x(mark(x0), s(tt)), mark(x0)), A__X(mark(x0), mark(s(tt))), MARK(x0)) A__X(x0, s(s(0))) -> c7(A__PLUS(a__x(mark(x0), s(0)), mark(x0)), A__X(mark(x0), mark(s(0))), MARK(x0)) A__X(x0, s(s(s(z0)))) -> c7(A__PLUS(a__x(mark(x0), s(s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(s(s(z0)))), MARK(x0)) A__X(and(z0, z1), s(s(x1))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), s(mark(x1))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(s(x1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(s(x1))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), s(mark(x1))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(s(x1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(s(x1))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), s(mark(x1))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(s(x1))), MARK(x(z0, z1))) A__X(s(z0), s(s(x1))) -> c7(A__PLUS(a__x(s(mark(z0)), s(mark(x1))), mark(s(z0))), A__X(mark(s(z0)), mark(s(x1))), MARK(s(z0))) A__X(x0, s(s(x1))) -> c7(A__X(mark(x0), mark(s(x1)))) A__X(tt, s(s(x1))) -> c7(A__X(mark(tt), mark(s(x1)))) A__X(0, s(s(x1))) -> c7(A__PLUS(a__x(mark(0), s(mark(x1))), 0), A__X(mark(0), mark(s(x1)))) A__X(tt, s(s(x1))) -> c7(A__PLUS(a__x(tt, s(mark(x1))), mark(tt)), A__X(mark(tt), mark(s(x1)))) A__X(0, s(s(x1))) -> c7(A__PLUS(a__x(0, s(mark(x1))), mark(0)), A__X(mark(0), mark(s(x1)))) A__X(and(x0, z1), s(x2)) -> c7(A__PLUS(a__x(and(mark(x0), z1), mark(x2)), mark(and(x0, z1))), A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(a__and(a__and(mark(z0), z1), x1), mark(x2)), mark(and(and(z0, z1), x1))), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), mark(and(plus(z0, z1), x1))), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), mark(and(x(z0, z1), x1))), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(a__and(tt, x1), mark(x2)), mark(and(tt, x1))), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(a__and(s(mark(z0)), x1), mark(x2)), mark(and(s(z0), x1))), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(a__and(0, x1), mark(x2)), mark(and(0, x1))), A__X(mark(and(0, x1)), mark(x2))) S tuples: A__AND(tt, z0) -> c(MARK(z0)) A__PLUS(z0, 0) -> c2(MARK(z0)) MARK(s(z0)) -> c18(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)) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(tt, s(x1)) -> c7(A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(x0, s(x1)) -> c8(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), A__X(mark(x0), mark(x1)), MARK(x1)) A__X(x0, s(and(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(x0, s(plus(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x0, s(x(z0, z1))) -> c8(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(x0, s(s(z0))) -> c8(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(s(z0))) A__X(and(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(x1)) A__X(plus(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(x1)) A__X(x(z0, z1), s(x1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__PLUS(a__x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1)), MARK(x1)) A__X(0, s(x1)) -> c8(A__PLUS(a__x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1)), MARK(x1)) A__X(s(z0), s(x1)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(x1)) A__X(tt, s(x1)) -> c8(A__X(mark(tt), mark(x1)), MARK(x1)) A__X(x0, s(tt)) -> c8(A__PLUS(a__x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt))) A__X(x0, s(0)) -> c8(A__PLUS(a__x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0))) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(and(z0, z1)), mark(x1)), a__and(mark(z0), z1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x1)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x1)), s(mark(z0))), MARK(s(z0))) A__X(x0, s(x1)) -> c9(A__PLUS(x(mark(x0), mark(x1)), mark(x0)), MARK(x0)) A__X(x0, s(and(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x0)), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c9(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0)) A__X(x0, s(tt)) -> c9(A__PLUS(a__x(mark(x0), tt), mark(x0)), MARK(x0)) A__X(x0, s(0)) -> c9(A__PLUS(a__x(mark(x0), 0), mark(x0)), MARK(x0)) A__X(x0, s(s(z0))) -> c9(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x0)), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(s(z0))), MARK(s(z0))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(mark(0), mark(x1)), 0)) A__X(tt, s(x1)) -> c9(A__PLUS(a__x(tt, mark(x1)), mark(tt))) A__X(0, s(x1)) -> c9(A__PLUS(a__x(0, mark(x1)), mark(0))) MARK(and(and(z0, z1), x1)) -> c11(A__AND(a__and(mark(z0), z1), x1), MARK(and(z0, z1))) MARK(and(plus(z0, z1), x1)) -> c11(A__AND(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(and(x(z0, z1), x1)) -> c11(A__AND(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(and(tt, x1)) -> c11(A__AND(tt, x1)) MARK(and(s(z0), x1)) -> c11(MARK(s(z0))) MARK(plus(x0, and(z0, z1))) -> c12(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c12(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c12(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, 0)) -> c12(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(x0, s(z0))) -> c12(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(and(z0, z1), x1)) -> c12(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(plus(plus(z0, z1), x1)) -> c12(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(x(z0, z1), x1)) -> c12(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c12(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c12(MARK(x0)) MARK(plus(tt, x1)) -> c12(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c12(A__PLUS(0, mark(x1))) MARK(plus(x0, and(z0, z1))) -> c13(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) MARK(plus(x0, plus(z0, z1))) -> c13(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, x(z0, z1))) -> c13(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c13(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(and(z0, z1), x1)) -> c13(A__PLUS(a__and(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c13(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c13(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c13(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c13(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c13(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c13(A__PLUS(mark(x0), 0)) MARK(x(x0, and(z0, z1))) -> c14(A__X(mark(x0), a__and(mark(z0), z1)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c14(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c14(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c14(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(and(z0, z1), x1)) -> c14(A__X(a__and(mark(z0), z1), mark(x1)), MARK(and(z0, z1))) MARK(x(plus(z0, z1), x1)) -> c14(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(x(z0, z1), x1)) -> c14(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c14(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c14(MARK(x0)) MARK(x(x0, 0)) -> c14(MARK(x0)) MARK(x(tt, x1)) -> c14(A__X(tt, 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c4(A__PLUS(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), MARK(plus(x(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(x(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__x(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(x(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), MARK(x(x1, and(z0, z1)))) A__PLUS(x0, s(x(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(x(x1, plus(z0, z1)))) A__PLUS(x0, s(x(x1, x(z0, z1)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), MARK(x(x1, x(z0, z1)))) A__PLUS(x0, s(x(x1, tt))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), tt)), MARK(x(x1, tt))) A__PLUS(x0, s(x(x1, 0))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), 0)), MARK(x(x1, 0))) A__PLUS(x0, s(x(x1, s(z0)))) -> c4(A__PLUS(mark(x0), a__x(mark(x1), s(mark(z0)))), MARK(x(x1, s(z0)))) A__PLUS(x0, s(x(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), MARK(x(and(z0, z1), x2))) A__PLUS(x0, s(x(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), MARK(x(plus(z0, z1), x2))) A__PLUS(x0, s(x(x(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), MARK(x(x(z0, z1), x2))) A__PLUS(x0, s(x(tt, x2))) -> c4(A__PLUS(mark(x0), a__x(tt, mark(x2))), MARK(x(tt, x2))) A__PLUS(x0, s(x(0, x2))) -> c4(A__PLUS(mark(x0), a__x(0, mark(x2))), MARK(x(0, x2))) A__PLUS(x0, s(x(s(z0), x2))) -> c4(A__PLUS(mark(x0), a__x(s(mark(z0)), mark(x2))), MARK(x(s(z0), x2))) A__PLUS(and(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(plus(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x(z0, z1), s(x(x1, x2))) -> c4(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(tt, s(x(x1, x2))) -> c4(A__PLUS(tt, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(0, s(x(x1, x2))) -> c4(A__PLUS(0, a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(s(z0), s(x(x1, x2))) -> c4(A__PLUS(s(mark(z0)), a__x(mark(x1), mark(x2))), MARK(x(x1, x2))) A__PLUS(x0, s(x(x1, x2))) -> c4(MARK(x(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(x(z0, z1)))) -> c4(A__PLUS(mark(x0), s(a__x(mark(z0), mark(z1)))), MARK(s(x(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(x(z0, z1), s(s(x1))) -> c4(A__PLUS(a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__and(a__x(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, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__plus(mark(x0), a__x(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(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__plus(a__x(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(x(x0, x1), s(x2)) -> c4(A__PLUS(x(mark(x0), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, and(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__and(mark(z0), z1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, plus(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, x(z0, z1)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), a__x(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__PLUS(x(x0, tt), s(x2)) -> c4(A__PLUS(a__x(mark(x0), tt), mark(x2)), MARK(x2)) A__PLUS(x(x0, 0), s(x2)) -> c4(A__PLUS(a__x(mark(x0), 0), mark(x2)), MARK(x2)) A__PLUS(x(x0, s(z0)), s(x2)) -> c4(A__PLUS(a__x(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) A__PLUS(x(and(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__and(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(plus(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x(z0, z1), x1), s(x2)) -> c4(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(tt, x1), s(x2)) -> c4(A__PLUS(a__x(tt, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(0, x1), s(x2)) -> c4(A__PLUS(a__x(0, mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(s(z0), x1), s(x2)) -> c4(A__PLUS(a__x(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) A__PLUS(x(x0, x1), s(0)) -> c4(A__PLUS(a__x(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(x(z0, z1)), s(x1)) -> c4(A__PLUS(s(a__x(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)) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(and(z0, z1), x1)), mark(x2)), a__and(a__and(mark(z0), z1), x1)), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(plus(z0, z1), x1)), mark(x2)), a__and(a__plus(mark(z0), mark(z1)), x1)), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(x(z0, z1), x1)), mark(x2)), a__and(a__x(mark(z0), mark(z1)), x1)), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(tt, x1)), mark(x2)), a__and(tt, x1)), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(s(z0), x1)), mark(x2)), a__and(s(mark(z0)), x1)), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(and(x0, x1)), mark(x2)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x2)), MARK(and(x0, x1))) A__X(and(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__and(mark(z0), z1)), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(and(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__plus(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(plus(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), a__x(mark(z0), mark(z1))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(x(z0, z1))), MARK(and(x0, x1))) A__X(and(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), tt), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(tt)), MARK(and(x0, x1))) A__X(and(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(and(x0, x1)), 0), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(0)), MARK(and(x0, x1))) A__X(and(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(and(x0, x1)), s(mark(z0))), a__and(mark(x0), x1)), A__X(mark(and(x0, x1)), mark(s(z0))), MARK(and(x0, x1))) A__X(and(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), mark(x2)), a__and(mark(z0), z1)), A__X(mark(and(z0, z1)), mark(x2)), MARK(and(z0, z1))) A__X(and(x0, z1), s(x2)) -> c7(A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(and(0, x1)), mark(x2)), a__and(0, x1)), A__X(mark(and(0, x1)), mark(x2))) A__X(plus(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, plus(z0, z1))), mark(x2)), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(plus(x0, plus(z0, z1))), mark(x2)), MARK(plus(x0, plus(z0, z1)))) A__X(plus(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, and(z0, z1))), mark(x2)), a__plus(mark(x0), a__and(mark(z0), z1))), A__X(mark(plus(x0, and(z0, z1))), mark(x2)), MARK(plus(x0, and(z0, z1)))) A__X(plus(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, x(z0, z1))), mark(x2)), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(plus(x0, x(z0, z1))), mark(x2)), MARK(plus(x0, x(z0, z1)))) A__X(plus(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, tt)), mark(x2)), a__plus(mark(x0), tt)), A__X(mark(plus(x0, tt)), mark(x2)), MARK(plus(x0, tt))) A__X(plus(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, 0)), mark(x2)), a__plus(mark(x0), 0)), A__X(mark(plus(x0, 0)), mark(x2)), MARK(plus(x0, 0))) A__X(plus(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x0, s(z0))), mark(x2)), a__plus(mark(x0), s(mark(z0)))), A__X(mark(plus(x0, s(z0))), mark(x2)), MARK(plus(x0, s(z0)))) A__X(plus(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(plus(z0, z1), x1)), mark(x2)), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(plus(z0, z1), x1)), mark(x2)), MARK(plus(plus(z0, z1), x1))) A__X(plus(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(and(z0, z1), x1)), mark(x2)), a__plus(a__and(mark(z0), z1), mark(x1))), A__X(mark(plus(and(z0, z1), x1)), mark(x2)), MARK(plus(and(z0, z1), x1))) A__X(plus(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(x(z0, z1), x1)), mark(x2)), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(plus(x(z0, z1), x1)), mark(x2)), MARK(plus(x(z0, z1), x1))) A__X(plus(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(tt, x1)), mark(x2)), a__plus(tt, mark(x1))), A__X(mark(plus(tt, x1)), mark(x2)), MARK(plus(tt, x1))) A__X(plus(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(0, x1)), mark(x2)), a__plus(0, mark(x1))), A__X(mark(plus(0, x1)), mark(x2)), MARK(plus(0, x1))) A__X(plus(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(plus(s(z0), x1)), mark(x2)), a__plus(s(mark(z0)), mark(x1))), A__X(mark(plus(s(z0), x1)), mark(x2)), MARK(plus(s(z0), x1))) A__X(plus(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(plus(x0, x1)), mark(x2)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__plus(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(plus(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__and(mark(z0), z1)), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(and(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), a__x(mark(z0), mark(z1))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(x(z0, z1))), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), tt), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(tt)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), 0), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(0)), MARK(plus(x0, x1))) A__X(plus(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(plus(x0, x1)), s(mark(z0))), a__plus(mark(x0), mark(x1))), A__X(mark(plus(x0, x1)), mark(s(z0))), MARK(plus(x0, x1))) A__X(plus(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x2)), MARK(plus(z0, z1))) A__X(plus(x0, x1), s(x2)) -> c7(A__X(mark(plus(x0, x1)), mark(x2)), MARK(plus(x0, x1))) A__X(x(x0, x(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, x(z0, z1))), mark(x2)), a__x(mark(x0), a__x(mark(z0), mark(z1)))), A__X(mark(x(x0, x(z0, z1))), mark(x2)), MARK(x(x0, x(z0, z1)))) A__X(x(x0, and(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, and(z0, z1))), mark(x2)), a__x(mark(x0), a__and(mark(z0), z1))), A__X(mark(x(x0, and(z0, z1))), mark(x2)), MARK(x(x0, and(z0, z1)))) A__X(x(x0, plus(z0, z1)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, plus(z0, z1))), mark(x2)), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), A__X(mark(x(x0, plus(z0, z1))), mark(x2)), MARK(x(x0, plus(z0, z1)))) A__X(x(x0, tt), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, tt)), mark(x2)), a__x(mark(x0), tt)), A__X(mark(x(x0, tt)), mark(x2)), MARK(x(x0, tt))) A__X(x(x0, 0), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, 0)), mark(x2)), a__x(mark(x0), 0)), A__X(mark(x(x0, 0)), mark(x2)), MARK(x(x0, 0))) A__X(x(x0, s(z0)), s(x2)) -> c7(A__PLUS(a__x(mark(x(x0, s(z0))), mark(x2)), a__x(mark(x0), s(mark(z0)))), A__X(mark(x(x0, s(z0))), mark(x2)), MARK(x(x0, s(z0)))) A__X(x(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(x(z0, z1), x1)), mark(x2)), a__x(a__x(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(x(z0, z1), x1)), mark(x2)), MARK(x(x(z0, z1), x1))) A__X(x(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(and(z0, z1), x1)), mark(x2)), a__x(a__and(mark(z0), z1), mark(x1))), A__X(mark(x(and(z0, z1), x1)), mark(x2)), MARK(x(and(z0, z1), x1))) A__X(x(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(plus(z0, z1), x1)), mark(x2)), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), A__X(mark(x(plus(z0, z1), x1)), mark(x2)), MARK(x(plus(z0, z1), x1))) A__X(x(tt, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(tt, x1)), mark(x2)), a__x(tt, mark(x1))), A__X(mark(x(tt, x1)), mark(x2)), MARK(x(tt, x1))) A__X(x(0, x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(0, x1)), mark(x2)), a__x(0, mark(x1))), A__X(mark(x(0, x1)), mark(x2)), MARK(x(0, x1))) A__X(x(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(mark(x(s(z0), x1)), mark(x2)), a__x(s(mark(z0)), mark(x1))), A__X(mark(x(s(z0), x1)), mark(x2)), MARK(x(s(z0), x1))) A__X(x(x0, x1), s(x2)) -> c7(A__PLUS(x(mark(x(x0, x1)), mark(x2)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(x(x0, x1), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__x(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(x(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__and(mark(z0), z1)), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(and(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), a__plus(mark(z0), mark(z1))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(plus(z0, z1))), MARK(x(x0, x1))) A__X(x(x0, x1), s(tt)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), tt), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(tt)), MARK(x(x0, x1))) A__X(x(x0, x1), s(0)) -> c7(A__PLUS(a__x(mark(x(x0, x1)), 0), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(0)), MARK(x(x0, x1))) A__X(x(x0, x1), s(s(z0))) -> c7(A__PLUS(a__x(mark(x(x0, x1)), s(mark(z0))), a__x(mark(x0), mark(x1))), A__X(mark(x(x0, x1)), mark(s(z0))), MARK(x(x0, x1))) A__X(x(z0, z1), s(x2)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x2)), MARK(x(z0, z1))) A__X(x(x0, x1), s(x2)) -> c7(A__X(mark(x(x0, x1)), mark(x2)), MARK(x(x0, x1))) A__X(s(s(z0)), s(x1)) -> c7(A__PLUS(a__x(mark(s(s(z0))), mark(x1)), s(s(mark(z0)))), A__X(mark(s(s(z0))), mark(x1)), MARK(s(s(z0)))) A__X(s(and(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(and(z0, z1))), mark(x1)), s(a__and(mark(z0), z1))), A__X(mark(s(and(z0, z1))), mark(x1)), MARK(s(and(z0, z1)))) A__X(s(plus(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(plus(z0, z1))), mark(x1)), s(a__plus(mark(z0), mark(z1)))), A__X(mark(s(plus(z0, z1))), mark(x1)), MARK(s(plus(z0, z1)))) A__X(s(x(z0, z1)), s(x1)) -> c7(A__PLUS(a__x(mark(s(x(z0, z1))), mark(x1)), s(a__x(mark(z0), mark(z1)))), A__X(mark(s(x(z0, z1))), mark(x1)), MARK(s(x(z0, z1)))) A__X(s(tt), s(x1)) -> c7(A__PLUS(a__x(mark(s(tt)), mark(x1)), s(tt)), A__X(mark(s(tt)), mark(x1)), MARK(s(tt))) A__X(s(0), s(x1)) -> c7(A__PLUS(a__x(mark(s(0)), mark(x1)), s(0)), A__X(mark(s(0)), mark(x1)), MARK(s(0))) A__X(s(x0), s(x1)) -> c7(A__PLUS(x(mark(s(x0)), mark(x1)), s(mark(x0))), A__X(mark(s(x0)), mark(x1)), MARK(s(x0))) A__X(s(x0), s(s(z0))) -> c7(A__PLUS(a__x(mark(s(x0)), s(mark(z0))), s(mark(x0))), A__X(mark(s(x0)), mark(s(z0))), MARK(s(x0))) A__X(s(x0), s(and(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__and(mark(z0), z1)), s(mark(x0))), A__X(mark(s(x0)), mark(and(z0, z1))), MARK(s(x0))) A__X(s(x0), s(plus(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__plus(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(plus(z0, z1))), MARK(s(x0))) A__X(s(x0), s(x(z0, z1))) -> c7(A__PLUS(a__x(mark(s(x0)), a__x(mark(z0), mark(z1))), s(mark(x0))), A__X(mark(s(x0)), mark(x(z0, z1))), MARK(s(x0))) A__X(s(x0), s(tt)) -> c7(A__PLUS(a__x(mark(s(x0)), tt), s(mark(x0))), A__X(mark(s(x0)), mark(tt)), MARK(s(x0))) A__X(s(x0), s(0)) -> c7(A__PLUS(a__x(mark(s(x0)), 0), s(mark(x0))), A__X(mark(s(x0)), mark(0)), MARK(s(x0))) A__X(s(z0), s(x1)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x1)), s(mark(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(x0, s(and(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__and(mark(z0), z1)), mark(x0)), A__X(mark(x0), mark(and(z0, z1))), MARK(x0)) A__X(x0, s(plus(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__plus(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(plus(z0, z1))), MARK(x0)) A__X(x0, s(x(z0, z1))) -> c7(A__PLUS(x(mark(x0), a__x(mark(z0), mark(z1))), mark(x0)), A__X(mark(x0), mark(x(z0, z1))), MARK(x0)) A__X(x0, s(tt)) -> c7(A__PLUS(x(mark(x0), tt), mark(x0)), A__X(mark(x0), mark(tt)), MARK(x0)) A__X(x0, s(0)) -> c7(A__PLUS(x(mark(x0), 0), mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(x0, s(s(z0))) -> c7(A__PLUS(x(mark(x0), s(mark(z0))), mark(x0)), A__X(mark(x0), mark(s(z0))), MARK(x0)) A__X(and(z0, z1), s(x1)) -> c7(A__PLUS(x(a__and(mark(z0), z1), mark(x1)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x1)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x1)) -> c7(A__PLUS(x(a__plus(mark(z0), mark(z1)), mark(x1)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x1)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x1)) -> c7(A__PLUS(x(a__x(mark(z0), mark(z1)), mark(x1)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x1)), MARK(x(z0, z1))) A__X(s(z0), s(x1)) -> c7(A__PLUS(x(s(mark(z0)), mark(x1)), mark(s(z0))), A__X(mark(s(z0)), mark(x1)), MARK(s(z0))) A__X(0, s(x1)) -> c7(A__PLUS(x(mark(0), mark(x1)), 0), A__X(mark(0), mark(x1))) A__X(tt, s(x1)) -> c7(A__PLUS(x(tt, mark(x1)), mark(tt)), A__X(mark(tt), mark(x1))) A__X(0, s(x1)) -> c7(A__PLUS(x(0, mark(x1)), mark(0)), A__X(mark(0), mark(x1))) A__X(x0, s(and(x1, z1))) -> c7(A__PLUS(a__x(mark(x0), and(mark(x1), z1)), mark(x0)), A__X(mark(x0), mark(and(x1, z1))), MARK(x0)) A__X(x0, s(and(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__and(mark(z0), z1), x2)), mark(x0)), A__X(mark(x0), mark(and(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(a__x(mark(z0), mark(z1)), x2)), mark(x0)), A__X(mark(x0), mark(and(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(and(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(tt, x2)), mark(x0)), A__X(mark(x0), mark(and(tt, x2))), MARK(x0)) A__X(x0, s(and(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(0, x2)), mark(x0)), A__X(mark(x0), mark(and(0, x2))), MARK(x0)) A__X(x0, s(and(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__and(s(mark(z0)), x2)), mark(x0)), A__X(mark(x0), mark(and(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__and(mark(x1), x2)), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(and(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(and(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(and(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__and(mark(x1), x2)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(and(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(and(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__and(mark(x1), x2)), mark(s(z0))), A__X(mark(s(z0)), mark(and(x1, x2))), MARK(s(z0))) A__X(x0, s(and(x1, x2))) -> c7(A__X(mark(x0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__and(mark(x1), x2)), 0), A__X(mark(0), mark(and(x1, x2)))) A__X(tt, s(and(x1, x2))) -> c7(A__PLUS(a__x(tt, a__and(mark(x1), x2)), mark(tt)), A__X(mark(tt), mark(and(x1, x2)))) A__X(0, s(and(x1, x2))) -> c7(A__PLUS(a__x(0, a__and(mark(x1), x2)), mark(0)), A__X(mark(0), mark(and(x1, x2)))) A__X(x0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), plus(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x1, x2))), MARK(x0)) A__X(x0, s(plus(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(plus(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(plus(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(plus(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(plus(x1, tt))), MARK(x0)) A__X(x0, s(plus(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(plus(x1, 0))), MARK(x0)) A__X(x0, s(plus(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__plus(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(plus(x1, s(z0)))), MARK(x0)) A__X(x0, s(plus(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(plus(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(tt, x2))), MARK(x0)) A__X(x0, s(plus(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(0, x2))), MARK(x0)) A__X(x0, s(plus(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__plus(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(plus(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(plus(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(plus(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(plus(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(plus(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(plus(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__plus(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(plus(x1, x2))), MARK(s(z0))) A__X(x0, s(plus(x1, x2))) -> c7(A__X(mark(x0), mark(plus(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__plus(mark(x1), mark(x2))), 0), A__X(mark(0), mark(plus(x1, x2)))) A__X(tt, s(plus(x1, x2))) -> c7(A__PLUS(a__x(tt, a__plus(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(plus(x1, x2)))) A__X(0, s(plus(x1, x2))) -> c7(A__PLUS(a__x(0, a__plus(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(plus(x1, x2)))) A__X(x0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(x0), x(mark(x1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x1, x2))), MARK(x0)) A__X(x0, s(x(x1, and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(x(x1, and(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, plus(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(x(x1, x(z0, z1)))), MARK(x0)) A__X(x0, s(x(x1, tt))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), tt)), mark(x0)), A__X(mark(x0), mark(x(x1, tt))), MARK(x0)) A__X(x0, s(x(x1, 0))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), 0)), mark(x0)), A__X(mark(x0), mark(x(x1, 0))), MARK(x0)) A__X(x0, s(x(x1, s(z0)))) -> c7(A__PLUS(a__x(mark(x0), a__x(mark(x1), s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(x(x1, s(z0)))), MARK(x0)) A__X(x0, s(x(and(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__and(mark(z0), z1), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(and(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(plus(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__plus(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(plus(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(x(z0, z1), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(a__x(mark(z0), mark(z1)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(x(z0, z1), x2))), MARK(x0)) A__X(x0, s(x(tt, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(tt, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(tt, x2))), MARK(x0)) A__X(x0, s(x(0, x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(0, mark(x2))), mark(x0)), A__X(mark(x0), mark(x(0, x2))), MARK(x0)) A__X(x0, s(x(s(z0), x2))) -> c7(A__PLUS(a__x(mark(x0), a__x(s(mark(z0)), mark(x2))), mark(x0)), A__X(mark(x0), mark(x(s(z0), x2))), MARK(x0)) A__X(and(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), a__x(mark(x1), mark(x2))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(x(x1, x2))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x(x1, x2))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(x(x1, x2))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), a__x(mark(x1), mark(x2))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x(x1, x2))), MARK(x(z0, z1))) A__X(s(z0), s(x(x1, x2))) -> c7(A__PLUS(a__x(s(mark(z0)), a__x(mark(x1), mark(x2))), mark(s(z0))), A__X(mark(s(z0)), mark(x(x1, x2))), MARK(s(z0))) A__X(x0, s(x(x1, x2))) -> c7(A__X(mark(x0), mark(x(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__X(mark(tt), mark(x(x1, x2)))) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(mark(0), a__x(mark(x1), mark(x2))), 0), A__X(mark(0), mark(x(x1, x2)))) A__X(tt, s(x(x1, x2))) -> c7(A__PLUS(a__x(tt, a__x(mark(x1), mark(x2))), mark(tt)), A__X(mark(tt), mark(x(x1, x2)))) A__X(0, s(x(x1, x2))) -> c7(A__PLUS(a__x(0, a__x(mark(x1), mark(x2))), mark(0)), A__X(mark(0), mark(x(x1, x2)))) A__X(and(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), tt), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(tt)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), tt), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(tt)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(tt)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), tt), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(tt)), MARK(x(z0, z1))) A__X(s(z0), s(tt)) -> c7(A__PLUS(a__x(s(mark(z0)), tt), mark(s(z0))), A__X(mark(s(z0)), mark(tt)), MARK(s(z0))) A__X(x0, s(tt)) -> c7(A__X(mark(x0), mark(tt))) A__X(tt, s(tt)) -> c7(A__X(mark(tt), mark(tt))) A__X(0, s(tt)) -> c7(A__PLUS(a__x(mark(0), tt), 0), A__X(mark(0), mark(tt))) A__X(tt, s(tt)) -> c7(A__PLUS(a__x(tt, tt), mark(tt)), A__X(mark(tt), mark(tt))) A__X(0, s(tt)) -> c7(A__PLUS(a__x(0, tt), mark(0)), A__X(mark(0), mark(tt))) A__X(x0, s(0)) -> c7(A__PLUS(0, mark(x0)), A__X(mark(x0), mark(0)), MARK(x0)) A__X(and(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), 0), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(0)), MARK(and(z0, z1))) A__X(plus(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), 0), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(0)), MARK(plus(z0, z1))) A__X(x(z0, z1), s(0)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), 0), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(0)), MARK(x(z0, z1))) A__X(s(z0), s(0)) -> c7(A__PLUS(a__x(s(mark(z0)), 0), mark(s(z0))), A__X(mark(s(z0)), mark(0)), MARK(s(z0))) A__X(x0, s(0)) -> c7(A__X(mark(x0), mark(0))) A__X(tt, s(0)) -> c7(A__X(mark(tt), mark(0))) A__X(0, s(0)) -> c7(A__PLUS(a__x(mark(0), 0), 0), A__X(mark(0), mark(0))) A__X(tt, s(0)) -> c7(A__PLUS(a__x(tt, 0), mark(tt)), A__X(mark(tt), mark(0))) A__X(0, s(0)) -> c7(A__PLUS(a__x(0, 0), mark(0)), A__X(mark(0), mark(0))) A__X(x0, s(s(x1))) -> c7(A__PLUS(a__plus(a__x(mark(mark(x0)), mark(mark(x1))), mark(mark(x0))), mark(x0)), A__X(mark(x0), mark(s(x1))), MARK(x0)) A__X(x0, s(s(and(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), s(a__and(mark(z0), z1))), mark(x0)), A__X(mark(x0), mark(s(and(z0, z1)))), MARK(x0)) A__X(x0, s(s(plus(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), s(a__plus(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(s(plus(z0, z1)))), MARK(x0)) A__X(x0, s(s(x(z0, z1)))) -> c7(A__PLUS(a__x(mark(x0), s(a__x(mark(z0), mark(z1)))), mark(x0)), A__X(mark(x0), mark(s(x(z0, z1)))), MARK(x0)) A__X(x0, s(s(tt))) -> c7(A__PLUS(a__x(mark(x0), s(tt)), mark(x0)), A__X(mark(x0), mark(s(tt))), MARK(x0)) A__X(x0, s(s(0))) -> c7(A__PLUS(a__x(mark(x0), s(0)), mark(x0)), A__X(mark(x0), mark(s(0))), MARK(x0)) A__X(x0, s(s(s(z0)))) -> c7(A__PLUS(a__x(mark(x0), s(s(mark(z0)))), mark(x0)), A__X(mark(x0), mark(s(s(z0)))), MARK(x0)) A__X(and(z0, z1), s(s(x1))) -> c7(A__PLUS(a__x(a__and(mark(z0), z1), s(mark(x1))), mark(and(z0, z1))), A__X(mark(and(z0, z1)), mark(s(x1))), MARK(and(z0, z1))) A__X(plus(z0, z1), s(s(x1))) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), s(mark(x1))), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(s(x1))), MARK(plus(z0, z1))) A__X(x(z0, z1), s(s(x1))) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), s(mark(x1))), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(s(x1))), MARK(x(z0, z1))) A__X(s(z0), s(s(x1))) -> c7(A__PLUS(a__x(s(mark(z0)), s(mark(x1))), mark(s(z0))), A__X(mark(s(z0)), mark(s(x1))), MARK(s(z0))) A__X(x0, s(s(x1))) -> c7(A__X(mark(x0), mark(s(x1)))) A__X(tt, s(s(x1))) -> c7(A__X(mark(tt), mark(s(x1)))) A__X(0, s(s(x1))) -> c7(A__PLUS(a__x(mark(0), s(mark(x1))), 0), A__X(mark(0), mark(s(x1)))) A__X(tt, s(s(x1))) -> c7(A__PLUS(a__x(tt, s(mark(x1))), mark(tt)), A__X(mark(tt), mark(s(x1)))) A__X(0, s(s(x1))) -> c7(A__PLUS(a__x(0, s(mark(x1))), mark(0)), A__X(mark(0), mark(s(x1)))) A__X(and(x0, z1), s(x2)) -> c7(A__PLUS(a__x(and(mark(x0), z1), mark(x2)), mark(and(x0, z1))), A__X(mark(and(x0, z1)), mark(x2)), MARK(and(x0, z1))) A__X(and(and(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(a__and(a__and(mark(z0), z1), x1), mark(x2)), mark(and(and(z0, z1), x1))), A__X(mark(and(and(z0, z1), x1)), mark(x2)), MARK(and(and(z0, z1), x1))) A__X(and(plus(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(a__and(a__plus(mark(z0), mark(z1)), x1), mark(x2)), mark(and(plus(z0, z1), x1))), A__X(mark(and(plus(z0, z1), x1)), mark(x2)), MARK(and(plus(z0, z1), x1))) A__X(and(x(z0, z1), x1), s(x2)) -> c7(A__PLUS(a__x(a__and(a__x(mark(z0), mark(z1)), x1), mark(x2)), mark(and(x(z0, z1), x1))), A__X(mark(and(x(z0, z1), x1)), mark(x2)), MARK(and(x(z0, z1), x1))) A__X(and(tt, x1), s(x2)) -> c7(A__PLUS(a__x(a__and(tt, x1), mark(x2)), mark(and(tt, x1))), A__X(mark(and(tt, x1)), mark(x2)), MARK(and(tt, x1))) A__X(and(s(z0), x1), s(x2)) -> c7(A__PLUS(a__x(a__and(s(mark(z0)), x1), mark(x2)), mark(and(s(z0), x1))), A__X(mark(and(s(z0), x1)), mark(x2)), MARK(and(s(z0), x1))) A__X(and(0, x1), s(x2)) -> c7(A__PLUS(a__x(a__and(0, x1), mark(x2)), mark(and(0, x1))), A__X(mark(and(0, x1)), mark(x2))) K tuples:none Defined Rule Symbols: a__and_2, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__AND_2, A__PLUS_2, MARK_1, A__X_2 Compound Symbols: c_1, c2_1, c18_1, c3_2, c3_1, c4_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c14_2, c14_1, c15_2, c4_2