KILLED proof of input_Lb756VmtVc.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) NarrowingProof [BOTH BOUNDS(ID, ID), 45 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (14) CpxRNTS (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxRNTS (17) CompletionProof [UPPER BOUND(ID), 0 ms] (18) CpxTypedWeightedCompleteTrs (19) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (20) CpxRNTS (21) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (22) CdtProblem (23) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (24) CdtProblem (25) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (26) CdtProblem (27) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (28) CdtProblem (29) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 16 ms] (30) CdtProblem (31) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (32) CdtProblem (33) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (34) CdtProblem (35) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (36) CdtProblem (37) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (38) CdtProblem (39) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CdtProblem (41) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CdtProblem (43) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CdtProblem (45) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CdtProblem (47) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CdtProblem (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CdtProblem (51) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CdtProblem (53) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CdtProblem (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CdtProblem (57) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 2 ms] (62) CdtProblem (63) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9 ms] (70) CdtProblem (71) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 17 ms] (74) CdtProblem (75) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 43 ms] (78) CdtProblem (79) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 50 ms] (82) CdtProblem (83) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6 ms] (86) CdtProblem (87) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 76 ms] (94) CdtProblem (95) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 75 ms] (98) CdtProblem (99) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 13 ms] (102) CdtProblem (103) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 5 ms] (106) CdtProblem (107) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem (111) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 88 ms] (114) CdtProblem (115) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 139 ms] (118) CdtProblem (119) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 140 ms] (122) CdtProblem (123) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 97 ms] (126) CdtProblem (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 60 ms] (128) CdtProblem (129) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 29 ms] (130) CdtProblem (131) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 34 ms] (132) CdtProblem (133) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 92 ms] (134) CdtProblem (135) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 15 ms] (136) CdtProblem (137) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 26 ms] (138) CdtProblem (139) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 171 ms] (140) CdtProblem (141) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (144) CdtProblem (145) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 77 ms] (146) CdtProblem (147) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (148) CdtProblem (149) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 1 ms] (150) CdtProblem (151) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 47 ms] (152) CdtProblem (153) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (154) CdtProblem (155) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (156) CdtProblem (157) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 114 ms] (158) CdtProblem (159) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (160) CdtProblem (161) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (162) CdtProblem (163) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 147 ms] (164) CdtProblem (165) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 42 ms] (166) CdtProblem (167) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 160 ms] (168) CdtProblem (169) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 42 ms] (170) CdtProblem (171) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 181 ms] (172) CdtProblem (173) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (174) CdtProblem (175) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 171 ms] (176) CdtProblem (177) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 146 ms] (178) CdtProblem (179) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (180) CdtProblem (181) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 200 ms] (182) CdtProblem (183) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 64 ms] (184) CdtProblem (185) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 363 ms] (186) CdtProblem (187) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 95 ms] (188) CdtProblem (189) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 365 ms] (190) CdtProblem (191) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 18 ms] (192) CdtProblem (193) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 212 ms] (194) CdtProblem (195) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 15 ms] (196) CdtProblem (197) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 208 ms] (198) CdtProblem (199) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 47 ms] (200) CdtProblem (201) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 411 ms] (202) CdtProblem (203) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 97 ms] (204) CdtProblem (205) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 320 ms] (206) CdtProblem (207) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 75 ms] (208) 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) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (6) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__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 ---------------------------------------- (7) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (8) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__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 ---------------------------------------- (9) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: none (c) The following functions are completely defined: 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 ---------------------------------------- (10) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__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 ---------------------------------------- (11) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (12) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__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 ---------------------------------------- (13) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: tt => 1 0 => 0 ---------------------------------------- (14) Obligation: Complexity RNTS consisting of the following rules: a__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 ---------------------------------------- (15) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (16) Obligation: Complexity RNTS consisting of the following rules: a__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 ---------------------------------------- (17) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: none And the following fresh constants: none ---------------------------------------- (18) Obligation: Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__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 ---------------------------------------- (19) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: tt => 1 0 => 0 ---------------------------------------- (20) Obligation: Complexity RNTS consisting of the following rules: a__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. ---------------------------------------- (21) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (22) 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 ---------------------------------------- (23) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing nodes: A__X(z0, z1) -> c10 A__AND(z0, z1) -> c1 MARK(tt) -> c16 A__X(z0, 0) -> c6 A__PLUS(z0, z1) -> c5 MARK(0) -> c17 ---------------------------------------- (24) 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 ---------------------------------------- (25) 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))) ---------------------------------------- (26) 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 ---------------------------------------- (27) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (28) 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 ---------------------------------------- (29) 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)) ---------------------------------------- (30) 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 ---------------------------------------- (31) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__PLUS(x0, s(tt)) -> c4(A__PLUS(mark(x0), tt), MARK(tt)) ---------------------------------------- (32) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) 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 ---------------------------------------- (33) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (34) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) 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 ---------------------------------------- (35) 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))) ---------------------------------------- (36) 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 ---------------------------------------- (37) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (38) 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 ---------------------------------------- (39) 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)) ---------------------------------------- (40) 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 ---------------------------------------- (41) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (42) 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 ---------------------------------------- (43) 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))) ---------------------------------------- (44) 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 ---------------------------------------- (45) 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)) ---------------------------------------- (46) 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 ---------------------------------------- (47) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (48) 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 ---------------------------------------- (49) 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))) ---------------------------------------- (50) 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 ---------------------------------------- (51) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(and(0, x1)) -> c11(A__AND(0, x1), MARK(0)) ---------------------------------------- (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__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 ---------------------------------------- (53) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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)) 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 ---------------------------------------- (55) 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))) ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) 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 ---------------------------------------- (57) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) 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 ---------------------------------------- (59) 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)) ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) 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 ---------------------------------------- (61) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(x0, tt)) -> c13(A__PLUS(mark(x0), tt), MARK(tt)) ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) 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 ---------------------------------------- (63) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) 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 ---------------------------------------- (65) 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))) ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) 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 ---------------------------------------- (67) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) 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 ---------------------------------------- (69) 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)) ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) 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 ---------------------------------------- (71) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(x(x0, tt)) -> c15(A__X(mark(x0), tt), MARK(tt)) MARK(x(x0, 0)) -> c15(A__X(mark(x0), 0), MARK(0)) ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) 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 ---------------------------------------- (73) 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))) ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) 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 ---------------------------------------- (75) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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)) 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 ---------------------------------------- (77) 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))) ---------------------------------------- (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)) 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 ---------------------------------------- (79) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) 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 ---------------------------------------- (81) 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))) ---------------------------------------- (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)) 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 ---------------------------------------- (83) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) 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)), 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)))) 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 ---------------------------------------- (85) 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))) ---------------------------------------- (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)) 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)), 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))) 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 ---------------------------------------- (87) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 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)) 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))) 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)))) 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 ---------------------------------------- (89) 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))) ---------------------------------------- (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)) 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, 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(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 ---------------------------------------- (91) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) 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(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)), 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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(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 ---------------------------------------- (93) 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))) ---------------------------------------- (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(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))), 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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))) 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(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 ---------------------------------------- (95) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) 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), 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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))) 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))) -> 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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 ---------------------------------------- (97) 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))) ---------------------------------------- (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(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), 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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), 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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), 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(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 ---------------------------------------- (99) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) 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), 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))) 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 ---------------------------------------- (101) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(s(z0), s(x1)) -> c3(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) by A__PLUS(s(x0), s(and(z0, z1))) -> c3(A__PLUS(s(mark(x0)), a__and(mark(z0), z1)), MARK(s(x0))) A__PLUS(s(x0), s(plus(z0, z1))) -> c3(A__PLUS(s(mark(x0)), a__plus(mark(z0), mark(z1))), MARK(s(x0))) A__PLUS(s(x0), s(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))) ---------------------------------------- (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(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)) 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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), 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)) -> 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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 ---------------------------------------- (103) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) 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(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, 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), 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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)))) 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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))) 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 ---------------------------------------- (105) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(tt, s(x1)) -> c3(A__PLUS(tt, mark(x1))) by A__PLUS(tt, s(and(z0, z1))) -> c3(A__PLUS(tt, a__and(mark(z0), z1))) A__PLUS(tt, s(plus(z0, z1))) -> c3(A__PLUS(tt, a__plus(mark(z0), mark(z1)))) A__PLUS(tt, s(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)))) ---------------------------------------- (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(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(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)), 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), 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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(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 ---------------------------------------- (107) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__PLUS(tt, s(tt)) -> c3(A__PLUS(tt, tt)) ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) 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, 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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)), 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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 ---------------------------------------- (109) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(0, s(x1)) -> c3(A__PLUS(0, mark(x1))) by A__PLUS(0, s(and(z0, z1))) -> c3(A__PLUS(0, a__and(mark(z0), z1))) A__PLUS(0, s(plus(z0, z1))) -> c3(A__PLUS(0, a__plus(mark(z0), mark(z1)))) A__PLUS(0, s(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)))) ---------------------------------------- (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(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, 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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, 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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)), 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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 ---------------------------------------- (111) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__PLUS(0, s(tt)) -> c3(A__PLUS(0, tt)) ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) 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))) 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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 ---------------------------------------- (113) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(x0, s(and(z0, z1))) -> c4(A__PLUS(mark(x0), a__and(mark(z0), z1)), MARK(and(z0, z1))) by A__PLUS(x0, s(and(x1, z1))) -> c4(A__PLUS(mark(x0), and(mark(x1), z1)), MARK(and(x1, z1))) A__PLUS(x0, s(and(and(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__and(mark(z0), z1), x2)), MARK(and(and(z0, z1), x2))) A__PLUS(x0, s(and(plus(z0, z1), x2))) -> c4(A__PLUS(mark(x0), a__and(a__plus(mark(z0), mark(z1)), x2)), MARK(and(plus(z0, z1), x2))) A__PLUS(x0, s(and(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))) ---------------------------------------- (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(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))) -> 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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 ---------------------------------------- (115) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) 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)), 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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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), 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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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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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 ---------------------------------------- (117) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(x0, s(plus(z0, z1))) -> c4(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) by A__PLUS(x0, s(plus(x1, x2))) -> c4(A__PLUS(mark(x0), plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(x0, s(plus(x1, and(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__and(mark(z0), z1))), MARK(plus(x1, and(z0, z1)))) A__PLUS(x0, s(plus(x1, plus(z0, z1)))) -> c4(A__PLUS(mark(x0), a__plus(mark(x1), a__plus(mark(z0), mark(z1)))), MARK(plus(x1, plus(z0, z1)))) A__PLUS(x0, s(plus(x1, 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))) ---------------------------------------- (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(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)) -> 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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))) -> 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, 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 ---------------------------------------- (119) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) 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, 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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))) 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), 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))) 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) 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))) ---------------------------------------- (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(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, 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c4(A__PLUS(mark(x0), a__plus(s(mark(z0)), mark(x2))), MARK(plus(s(z0), x2))) A__PLUS(and(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__and(mark(z0), z1), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(plus(z0, z1), s(plus(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x1), mark(x2))), MARK(plus(x1, x2))) A__PLUS(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))) 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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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)))) 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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 ---------------------------------------- (123) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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)) -> 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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))) 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, 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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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 ---------------------------------------- (125) 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))) ---------------------------------------- (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(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), 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))) 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)), 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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))) 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(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)) ---------------------------------------- (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(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), 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-> 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(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), 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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), 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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(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 ---------------------------------------- (129) 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)) ---------------------------------------- (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(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)) 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 ---------------------------------------- (131) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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, 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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)) 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, 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 ---------------------------------------- (133) 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)) ---------------------------------------- (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(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))) 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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), 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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, 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)) 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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)) 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) 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)) ---------------------------------------- (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(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)))), 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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), 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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)))), 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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(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 ---------------------------------------- (137) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 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(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))) -> 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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), 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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))) 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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)) 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(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)) ---------------------------------------- (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(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))), 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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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 ---------------------------------------- (141) 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)) ---------------------------------------- (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(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)), 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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(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))), 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(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 ---------------------------------------- (143) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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(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)), 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)), 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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), 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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))) -> 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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)) 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) 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))) ---------------------------------------- (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(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), 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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, 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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), 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c4(A__PLUS(a__and(mark(z0), z1), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(plus(z0, z1), s(and(x1, x2))) -> c4(A__PLUS(a__plus(mark(z0), mark(z1)), a__and(mark(x1), x2)), MARK(and(x1, x2))) A__PLUS(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, 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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(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, 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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)), 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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 ---------------------------------------- (147) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__PLUS(tt, s(tt)) -> c4(A__PLUS(tt, tt), MARK(tt)) ---------------------------------------- (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(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))) 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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), 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), 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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), 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 ---------------------------------------- (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(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(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))) -> 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))) 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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)), 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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))) -> 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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)) 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(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))) ---------------------------------------- (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(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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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)))) 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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, 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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)) 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, 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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))) 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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(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 ---------------------------------------- (153) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__PLUS(0, s(tt)) -> c4(A__PLUS(0, tt), MARK(tt)) ---------------------------------------- (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(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)), 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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, 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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), 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), 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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), 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 ---------------------------------------- (155) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) 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)), 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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)) 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)) 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) 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)) ---------------------------------------- (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(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))) -> 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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(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, 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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(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 ---------------------------------------- (159) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__PLUS(s(x0), s(tt)) -> c4(A__PLUS(s(mark(x0)), tt), MARK(tt)) ---------------------------------------- (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(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)) -> 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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(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), 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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(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 ---------------------------------------- (161) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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)) 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)) -> 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)) 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 ---------------------------------------- (163) 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))) ---------------------------------------- (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(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)), 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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__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(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)), 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), 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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(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 ---------------------------------------- (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(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)) -> 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-> 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), 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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)) 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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))) -> 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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, 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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)) -> 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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))) 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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))) 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 ---------------------------------------- (167) 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))) ---------------------------------------- (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(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)) -> 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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, 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), 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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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 ---------------------------------------- (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(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), 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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)) 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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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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))) 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)), 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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)) 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 ---------------------------------------- (171) 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))) ---------------------------------------- (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(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)), 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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)))) 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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, 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))) -> 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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, 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 ---------------------------------------- (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(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, 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)) -> 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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))) 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 ---------------------------------------- (175) 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))) ---------------------------------------- (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(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)), 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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, 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, 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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))) 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 ---------------------------------------- (177) 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))) ---------------------------------------- (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(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), 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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))), 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, 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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)) -> 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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)))) 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 ---------------------------------------- (179) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (180) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) 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)))) -> 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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))) 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, 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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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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 ---------------------------------------- (181) 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)))) ---------------------------------------- (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(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)), 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, 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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, 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-> 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))), 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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 ---------------------------------------- (183) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (184) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) 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)) -> 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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, 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)) -> 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))) 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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 ---------------------------------------- (185) 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)))) ---------------------------------------- (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(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)) -> 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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(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)))) 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, 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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 ---------------------------------------- (187) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 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(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))) 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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), 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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, 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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))) -> 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))) -> 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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, 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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)), 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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))) -> 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))), 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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(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 ---------------------------------------- (189) 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)))) ---------------------------------------- (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(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), 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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(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), 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, 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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))) 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 ---------------------------------------- (191) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (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(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, 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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)))) 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, 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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))), 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)))) 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 ---------------------------------------- (193) 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))) ---------------------------------------- (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(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), 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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, 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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), 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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)))) 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))) 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 ---------------------------------------- (195) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (196) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) 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)) -> 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, 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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))) 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)) -> 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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(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))) 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 ---------------------------------------- (197) 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))) ---------------------------------------- (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(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)), 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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(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), 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, 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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(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 ---------------------------------------- (199) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 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(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)) -> 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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), 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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)) -> 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, 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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))), 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)) -> 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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 ---------------------------------------- (201) 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)))) ---------------------------------------- (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(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)) -> 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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(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)), 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)) -> 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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, 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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)))) 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 ---------------------------------------- (203) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (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(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), 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(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)) -> 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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(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)))) 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 ---------------------------------------- (205) 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))) ---------------------------------------- (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(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))) -> 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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, 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), 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)) -> 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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(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 ---------------------------------------- (207) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (208) Obligation: Complexity Dependency Tuples Problem Rules: a__and(tt, z0) -> mark(z0) a__and(z0, z1) -> and(z0, z1) a__plus(z0, 0) -> mark(z0) a__plus(z0, s(z1)) -> s(a__plus(mark(z0), mark(z1))) a__plus(z0, z1) -> plus(z0, z1) 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))) -> 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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)) 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))) 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, 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(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